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10. AE-RED: A Hyperspectral Unmixing Framework Powered by Deep Autoencoder and Regularization by Denoising

Author

Zhao, Min, Chen, Jie, and Dobigeon, Nicolas

Subjects
FOS: Computer and information sciences, Computer Vision and Pattern Recognition (cs.CV), Image and Video Processing (eess.IV), FOS: Electrical engineering, electronic engineering, information engineering, Computer Science - Computer Vision and Pattern Recognition, Electrical Engineering and Systems Science - Image and Video Processing
Abstract

Spectral unmixing has been extensively studied with a variety of methods and used in many applications. Recently, data-driven techniques with deep learning methods have obtained great attention to spectral unmixing for its superior learning ability to automatically learn the structure information. In particular, autoencoder based architectures are elaborately designed to solve blind unmixing and model complex nonlinear mixtures. Nevertheless, these methods perform unmixing task as blackboxes and lack of interpretability. On the other hand, conventional unmixing methods carefully design the regularizer to add explicit information, in which algorithms such as plug-and-play (PnP) strategies utilize off-the-shelf denoisers to plug powerful priors. In this paper, we propose a generic unmixing framework to integrate the autoencoder network with regularization by denoising (RED), named AE-RED. More specially, we decompose the unmixing optimized problem into two subproblems. The first one is solved using deep autoencoders to implicitly regularize the estimates and model the mixture mechanism. The second one leverages the denoiser to bring in the explicit information. In this way, both the characteristics of the deep autoencoder based unmixing methods and priors provided by denoisers are merged into our well-designed framework to enhance the unmixing performance. Experiment results on both synthetic and real data sets show the superiority of our proposed framework compared with state-of-the-art unmixing approaches.

Published
2023

11. Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inference

Author

Coeurdoux, Florentin, Dobigeon, Nicolas, and Chainais, Pierre

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, Statistics - Machine Learning, Computer Vision and Pattern Recognition (cs.CV), Computer Science - Computer Vision and Pattern Recognition, Machine Learning (stat.ML), Machine Learning (cs.LG)
Abstract

This paper introduces a stochastic plug-and-play (PnP) sampling algorithm that leverages variable splitting to efficiently sample from a posterior distribution. The algorithm based on split Gibbs sampling (SGS) draws inspiration from the alternating direction method of multipliers (ADMM). It divides the challenging task of posterior sampling into two simpler sampling problems. The first problem depends on the likelihood function, while the second is interpreted as a Bayesian denoising problem that can be readily carried out by a deep generative model. Specifically, for an illustrative purpose, the proposed method is implemented in this paper using state-of-the-art diffusion-based generative models. Akin to its deterministic PnP-based counterparts, the proposed method exhibits the great advantage of not requiring an explicit choice of the prior distribution, which is rather encoded into a pre-trained generative model. However, unlike optimization methods (e.g., PnP-ADMM) which generally provide only point estimates, the proposed approach allows conventional Bayesian estimators to be accompanied by confidence intervals at a reasonable additional computational cost. Experiments on commonly studied image processing problems illustrate the efficiency of the proposed sampling strategy. Its performance is compared to recent state-of-the-art optimization and sampling methods.

Published
2023

12. Probabilistic Simplex Component Analysis by Importance Sampling

Author

Granot, Nerya, Diskin, Tzvi, Dobigeon, Nicolas, and Wiesel, Ami

Subjects
Signal Processing (eess.SP), FOS: Electrical engineering, electronic engineering, information engineering, Electrical Engineering and Systems Science - Signal Processing
Abstract

In this paper we consider the problem of linear unmixing hidden random variables defined over the simplex with additive Gaussian noise, also known as probabilistic simplex component analysis (PRISM). Previous solutions to tackle this challenging problem were based on geometrical approaches or computationally intensive variational methods. In contrast, we propose a conventional expectation maximization (EM) algorithm which embeds importance sampling. For this purpose, the proposal distribution is chosen as a simple surrogate distribution of the target posterior that is guaranteed to lie in the simplex. This distribution is based on the Gaussian linear minimum mean squared error (LMMSE) approximation which is accurate at high signal-to-noise ratio. Numerical experiments in different settings demonstrate the advantages of this adaptive surrogate over state-of-the-art methods.

Published
2023

14. Sliced-Wasserstein normalizing flows: beyond maximum likelihood training

Author

Coeurdoux, Florentin, Dobigeon, Nicolas, Chainais, Pierre, Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), and Université Fédérale Toulouse Midi-Pyrénées

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, Artificial Intelligence (cs.AI), [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, Computer Science - Artificial Intelligence, Machine Learning (stat.ML), [INFO.INFO-NE]Computer Science [cs]/Neural and Evolutionary Computing [cs.NE], Machine Learning (cs.LG), [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning; International audience; Despite their advantages, normalizing flows generally suffer from several shortcomings including their tendency to generate unrealistic data (e.g., images) and their failing to detect out-of-distribution data. One reason for these deficiencies lies in the training strategy which traditionally exploits a maximum likelihood principle only. This paper proposes a new training paradigm based on a hybrid objective function combining the maximum likelihood principle (MLE) and a sliced-Wasserstein distance. Results obtained on synthetic toy examples and real image data sets show better generative abilities in terms of both likelihood and visual aspects of the generated samples. Reciprocally, the proposed approach leads to a lower likelihood of out-of-distribution data, demonstrating a greater data fidelity of the resulting flows.

Published
2022

15. Learning optimal transport between two empirical distributions with normalizing flows

Author

Coeurdoux, Florentin, Dobigeon, Nicolas, Chainais, Pierre, Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), and ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019)

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Optimal transport, Machine Learning (stat.ML), Normalizing flows, Machine Learning (cs.LG), Generative model, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

International audience; Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and original method to address the problem of transporting a finite set of samples associated with a first underlying unknown distribution towards another finite set of samples drawn from another unknown distribution. We show that a particular instance of invertible neural networks, namely the normalizing flows, can be used to approximate the solution of this OT problem between a pair of empirical distributions. To this aim, we propose to relax the Monge formulation of OT by replacing the equality constraint on the pushforward measure by the minimization of the corresponding Wasserstein distance. The push-forward operator to be retrieved is then restricted to be a normalizing flow which is trained by optimizing the resulting cost function. This approach allows the transport map to be discretized as a composition of functions. Each of these functions is associated to one sub-flow of the network, whose output provides intermediate steps of the transport between the original and target measures. This discretization yields also a set of intermediate barycenters between the two measures of interest. Experiments conducted on toy examples as well as a challenging task of unsupervised translation demonstrate the interest of the proposed method. Finally, some experiments show that the proposed approach leads to a good approximation of the true OT.

Published
2022

17. Spatial–Spectral Multiscale Sparse Unmixing for Hyperspectral Images.

Author

Ince, Taner and Dobigeon, Nicolas

Abstract

We propose a simple yet efficient sparse unmixing method for hyperspectral images. It exploits the spatial and spectral properties of hyperspectral images by designing a new regularization informed by multiscale analysis. The proposed approach consists of two steps. First, a sparse unmixing is conducted on a coarse hyperspectral image resulting from a spatial smoothing of the original data. The estimated coarse abundance map is subsequently used to design two weighting terms summarizing the spatial and spectral properties of the image. They are combined to define a sparse regularization embedded into a unmixing problem associated with the original hyperspectral image at full resolution. The performance of the proposed method is assessed with numerous experiments conducted on synthetic and real datasets. It is shown to compete favorably with state-of-the-art methods from the literature with lower computational complexity. [ABSTRACT FROM AUTHOR]

Published
2023
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18. CD-GAN: a robust fusion-based generative adversarial network for unsupervised remote sensing change detection with heterogeneous sensors

Author

Wang, Jin-Ju, Dobigeon, Nicolas, Chabert, Marie, Wang, Ding-Cheng, Huang, Ting-Zhu, and Huang, Jie

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, Computer Vision and Pattern Recognition (cs.CV), Image and Video Processing (eess.IV), FOS: Electrical engineering, electronic engineering, information engineering, Computer Science - Computer Vision and Pattern Recognition, Electrical Engineering and Systems Science - Image and Video Processing, Machine Learning (cs.LG)
Abstract

In the context of Earth observation, the detection of changes is performed from multitemporal images acquired by sensors with possibly different spatial and/or spectral resolutions or even different modalities (e.g. optical, radar). Even limiting to the optical modality, this task has proved to be challenging as soon as the sensors have different spatial and/or spectral resolutions. This paper proposes a novel unsupervised change detection method dedicated to images acquired with such so-called heterogeneous optical sensors. This method capitalizes on recent advances which frame the change detection problem into a robust fusion framework. More precisely, we show that a deep adversarial network designed and trained beforehand to fuse a pair of multiband optical images can be easily complemented by a network with the same architecture to perform change detection. The resulting overall architecture itself follows an adversarial strategy where the fusion network and the additional network are interpreted as essential building blocks of a generator. A comparison with state-of-the-art change detection methods demonstrates the versatility and the effectiveness of the proposed approach.

Published
2022

21. Successive Nonnegative Projection Algorithm for Linear Quadratic Mixtures (EUSIPCO 2020)

Author

Kervazo, Christophe, Gillis, Nicolas, Dobigeon, Nicolas, University of Mons [Belgium] (UMONS), Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Institut National Polytechnique (Toulouse) (Toulouse INP), Fonds de la Recherche Scientifique - FNRS and the Fonds Wetenschappelijk Onderzoek - Vlanderen (FWO) under EOS Project n° O005318F-RG47, EURASIP : European Association for Signal Processing, ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), and European Project: 679515,H2020,ERC-2015-STG,COLORAMAP(2016)

Subjects
Non-linear Hyperspectral Unmixing, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Non-linear Blind Source Separation, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Separability and Pure-Pixel Assumption, Nonnegative Matrix Factorization, Linear-Quadratic Models, [PHYS.PHYS.PHYS-DATA-AN]Physics [physics]/Physics [physics]/Data Analysis, Statistics and Probability [physics.data-an], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

International audience; In this work, we tackle the problem of hyperspectral unmixing by departing from the usual linear model and focusing on a linear-quadratic (LQ) one. The algorithm we propose, coined Successive Nonnegative Projection Algorithm for Linear Quadratic mixtures (SNPALQ), extends the Successive Nonnegative Projection Algorithm (SNPA), specifically designed to address the unmixing problem under a linear non-negative model and the pure-pixel assumption (a.k.a. near-separable assumption). By explicitly modeling the product terms inherent to the LQ model along the iterations of the SNPA scheme, the nonlinear contributions of the mixing are mitigated, thus improving the separation quality. The approach is shown to be relevant in realistic numerical experiments, which further highlight that SNPALQ is robust to noise.

Published
2021

22. Successive Nonnegative Projection Algorithm for Linear Quadratic Mixtures (iTWIST 2020)

Author

Kervazo, Christophe, Gillis, Nicolas, Dobigeon, Nicolas, University of Mons [Belgium] (UMONS), Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Institut National Polytechnique (Toulouse) (Toulouse INP), Fonds de la Recherche Scientifique - FNRS and the Fonds Wetenschappelijk Onderzoek - Vlanderen (FWO) under EOS Project n° O005318F-RG47, and European Project: 679515,H2020,ERC-2015-STG,COLORAMAP(2016)

Subjects
Non-linear Hyperspectral Unmixing, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Non-linear Blind Source Separation, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Separability and Pure-Pixel Assumption, Nonnegative Matrix Factorization, Linear-Quadratic Models, [PHYS.PHYS.PHYS-DATA-AN]Physics [physics]/Physics [physics]/Data Analysis, Statistics and Probability [physics.data-an], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

International audience; In this work, we tackle the problem of hyperspectral (HS) unmixing by departing from the usual linear model and focusing on a Linear-Quadratic (LQ) one. The proposed algorithm, referred to as Successive Nonnegative Projection Algorithm for Linear Quadratic mixtures (SNPALQ), extends the Successive Nonnegative Projection Algorithm (SNPA), designed to address the unmixing problem under a linear model. By explicitly modeling the product terms inherent to the LQ model along the iterations of the SNPA scheme, the nonlinear contributions in the mixing are mitigated, thus improving the separation quality. The approach is shown to be relevant in a realistic numerical experiment.

Published
2020

23. Reconstruction of partially sampled STEM-EELS images with atomic resolution

Author

Monier, Etienne, Oberlin, Thomas, Brun, Nathalie, Dobigeon, Nicolas, Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Laboratoire de Physique des Solides (LPS), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Institut National Polytechnique (Toulouse) (Toulouse INP), Nicolas Dobigeon, Toulouse INP, France, Cédric Févotte, CNRS, France, and Dobigeon, Nicolas

Subjects
[INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], [INFO.INFO-CV] Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], [INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [PHYS.PHYS.PHYS-DATA-AN] Physics [physics]/Physics [physics]/Data Analysis, Statistics and Probability [physics.data-an], [PHYS.PHYS.PHYS-DATA-AN]Physics [physics]/Physics [physics]/Data Analysis, Statistics and Probability [physics.data-an], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

International audience; Electron microscopy has shown to be a powerful tool to ana-lyze chemical composition of samples. However, acquiring a high qualityimage is hard due to radiation damages which limit the signal-to-noiseratio. One solution, considered in this work, consists in spatially partiallyacquiring the multi-band image and reconstructing it afterwards. Wepropose a reconstruction algorithm, referred to as Fourier sparsity in3D (FS3D), based on a regularization specifically tailored for atomicallyresolved images. Experiments show that the proposed FS3D method leadsto state-of-the-art results with a significantly lighter computational cost.

Published
2019

24. Semi-supervised linear spectral unmixing using a hierarchical Bayesian model for hyperspectral imagery

Author

Dobigeon, Nicolas, Tourneret, Jean-Yves, and Chein-I Chang

Subjects
Bayesian statistical decision theory -- Usage, Markov processes -- Analysis, Random noise theory -- Analysis, Signal processing -- Research, Digital signal processor, Business, Computers, Electronics, Electronics and electrical industries
Abstract

A hierarchical Bayesian model is presented for hyperspectral image unmixing. An extension of the algorithm is studied for mixtures with unknown numbers of spectral components belonging to a known library.

Published
2008

25. Joint segmentation of piecewise constant autoregressive processes by using a hierarchical model and a Bayesian sampling approach

Author

Dobigeon, Nicolas, Tourneret, Jean-Yves, and Davy, Manuel

Subjects
Bayesian statistical decision theory -- Usage, Markov processes -- Analysis, Signal processing -- Methods, Monte Carlo method -- Usage, Digital signal processor, Business, Computers, Electronics, Electronics and electrical industries
Abstract

A joint segmentation algorithm is proposed for piecewise constant autoregressive (AR) processes recorded by several independent sensors. The results are illustrated by several simulations conducted with synthetic signals and real arc-tracking and speech signals.

Published
2007

26. Joint segmentation of multivariate astronomical time series: Bayesian sampling with a hierarchical model

Author

Dobigeon, Nicolas, Tourneret, Jean-Yves, and Scargle, Jeffrey D.

Subjects
Poisson distribution -- Analysis, Photons -- Research, Bayesian statistical decision theory, Business, Computers, Electronics, Electronics and electrical industries
Abstract

Bayesian sampling algorithms are studied for segmenting single and multiple time series by obeying Poisson distributions with piecewise constant parameters. A Gibbs sampling strategy has allowed joint estimation of the unknown parameters and hyperparameters and the results obtained from synthetic and real photon counting data have shown the performance of the proposed algorithm.

Published
2007

28. High-Dimensional Gaussian Sampling: A Review and a Unifying Approach Based on a Stochastic Proximal Point Algorithm.

Author

Vono, Maxime, Dobigeon, Nicolas, and Chainais, Pierre

Subjects
*MARKOV chain Monte Carlo, *NUMERICAL solutions for linear algebra, *MATHEMATICAL optimization, *ALGORITHMS
Abstract

Efficient sampling from a high-dimensional Gaussian distribution is an old but high-stakes issue. Vanilla Cholesky samplers imply a computational cost and memory requirements that can rapidly become prohibitive in high dimensions. To tackle these issues, multiple methods have been proposed from different communities ranging from iterative numerical linear algebra to Markov chain Monte Carlo (MCMC) approaches. Surprisingly, no complete review and comparison of these methods has been conducted. This paper aims to review all these approaches by pointing out their differences, close relations, benefits, and limitations. In addition to reviewing the state of the art, this paper proposes a unifying Gaussian simulation framework by deriving a stochastic counterpart of the celebrated proximal point algorithm in optimization. This framework offers a novel and unifying revisiting of most of the existing MCMC approaches while also extending them. Guidelines to choosing the appropriate Gaussian simulation method for a given sampling problem in high dimensions are proposed and illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

Published
2022
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29. On variable splitting for Markov chain Monte Carlo

Author

Vono, Maxime, Dobigeon, Nicolas, Chainais, Pierre, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Ecole Centrale de Lille (FRANCE), Université de Lille (FRANCE), Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Institut National Polytechnique (Toulouse) (Toulouse INP), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Institut National Polytechnique de Toulouse - INPT (FRANCE), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Traitement du signal et de l'image, Markov chain Monte Carlo(MCMC) algorithms
Abstract

National audience; Variable splitting is an old but widely used technique whichaims at dividing an initial complicated optimization problem into simplersub-problems. In this work, we take inspiration from this variable splitting idea in order to build efficient Markov chain Monte Carlo(MCMC) algorithms. Starting from an initial complex target distribution,auxiliary variables are introduced such that the marginal distributionof interest matches the initial one asymptotically. In addition to havetheoretical guarantees, the benefits of such an asymptotically exact dataaugmentation (AXDA) are fourfold: (i) easier-to-sample full conditionaldistributions, (ii) possibility to embed while accelerating state-of-the-artMCMC approaches, (iii) possibility to distribute the inference and (iv)to respect data privacy issues. The proposed approach is illustrated onclassical image processing and statistical learning problems.

Published
2019

30. Reconstruction of partially sampled multi-band images - Application to EELS microscopy

Author

Monier, Etienne, Oberlin, Thomas, Brun, Nathalie, Tencé, Marcel, De Frutos, Maria, Dobigeon, Nicolas, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - INPT (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Université Paris-Sud 11 (FRANCE), and Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)

Subjects
Spectrum-image, Scanning transmission electron microscope (STEM), Image reconstruction, Inpainting, Traitement du signal et de l'image, Multi-band imaging, Electron energy loss spectroscopy (EELS), Partial sampling
Abstract

Electron microscopy has shown to be a very powerful tool to map the chemical nature of samples at various scales down to atomic resolution. However, many samples can not be analyzed with an acceptable signal-to-noise ratio because of the radiation damage induced by the electron beam. This is particularly crucial for electron energy loss spectroscopy (EELS) which acquires spectral-spatial data and requires high beam intensity. Since scanning transmission electron microscopes (STEM) are able to acquire data cubes by scanning the electron probe over the sample and recording a spectrum for each spatial position, it is possible to design the scan pattern and to sample only specific pixels. As a consequence, partial acquisition schemes are now conceivable, provided a reconstruction of the full data cube is conducted as a post-processing step. This paper proposes two reconstruction algorithms for multi-band images acquired by STEM-EELS which exploits the spectral structure and the spatial smoothness of the image. The performance of the proposed schemes is illustrated thanks to experiments conducted on a realistic phantom dataset as well as real EELS spectrum-images.

Published
2018

31. Provably Robust Blind Source Separation of Linear-Quadratic Near-Separable Mixtures.

Author

Kervazo, Christophe, Gillis, Nicolas, and Dobigeon, Nicolas

Subjects
BLIND source separation, MATRIX decomposition
Abstract

In this work, we consider the problem of blind source separation (BSS) by departing from the usual linear model and focusing on the linear-quadratic (LQ) one. We propose two provably robust and computationally tractable algorithms to tackle this problem under separability assumptions which require the sources to appear as samples in the data set. The first algorithm, referred to as SNPALQ, generalizes the successive nonnegative projection algorithm (SNPA), designed for linear BSS. By explicitly modeling the product terms inherent to the LQ model along the iterations of the SNPA scheme, the nonlinear contributions of the mixing are mitigated, thus improving the separation quality. SNPALQ is shown to be able to recover the ground truth factors that generated the data, even in the presence of noise. The second algorithm is a brute force (BF) algorithm, which can be used as a postprocessing step for SNPALQ. It then enables one to discard the spurious (mixed) samples extracted by SNPALQ, thus broadening its applicability. The BF is in turn shown to be robust to noise (under potentially easier-to-check conditions than those of SNPALQ). We show that SNPALQ with and without the BF postprocessing is relevant in realistic numerical experiments. [ABSTRACT FROM AUTHOR]

Published
2021
Full Text
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32. Unmixing dynamic PET images for voxel-based kinetic component analysis

Author

Cruz Cavalcanti, Yanna, Oberlin, Thomas, Dobigeon, Nicolas, Stute, Simon, Ribeiro, Maria, Tauber, Clovis, Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse Capitole (UT Capitole), Université Fédérale Toulouse Midi-Pyrénées, Institut National Polytechnique (Toulouse) (Toulouse INP), Imagerie Moléculaire in Vivo (IMIV - U1023 - ERL9218), Service Hospitalier Frédéric Joliot (SHFJ), Université Paris-Saclay-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Imagerie et cerveau (iBrain - Inserm U1253 - UNIV Tours ), Université de Tours (UT)-Institut National de la Santé et de la Recherche Médicale (INSERM), Dobigeon, Nicolas, Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM), Université de Tours-Institut National de la Santé et de la Recherche Médicale (INSERM), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
unmixing, [INFO.INFO-IM]Computer Science [cs]/Medical Imaging, [INFO.INFO-IM] Computer Science [cs]/Medical Imaging, brain imaging, deconvolution, Dynamic PET image, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing
Abstract

To analyze dynamic positron emission tomography (PET) images, various generic multivariate data analysis techniques have been considered in the literature, such as clustering, principal component analysis (PCA), independent component analysis (ICA) and non-negative matrix factorization (NMF). Nevertheless, these conventional approaches generally fail to recover a reliable, understandable and interpretable description of the data. In this paper, we propose an alternative analysis paradigm based on the concept of linear unmixing as an efficient and meaningful way to analyze dynamic PET images. The time-activity curves (TACs) measured in the voxels are modeled as linear combinations of elementary component signatures weighted by their respective concentrations in each voxel. Additionally to the non-negativity constraint of NMF, the proposed unmixing approach ensures an exhaustive description of the mixtures by a sum-to-one constraint of the mixing coefficients. Besides, it allows both the noise and partial volume effects to be handled. Moreover, the proposed method accounts for any possible fluctuations in the exchange rate of the tracer between the free compartment and a specifically bound ligand compartment. Indeed, it explicitly models the spatial variability of the corresponding signature through a perturbed specific binding component. The performance of the method is assessed on both synthetic and real data and compared to other conventional analysis methods.

Published
2017

33. Coupled dictionary learning for unsupervised change detection between multi-sensor remote sensing images

Author

Ferraris, Vinicius, Dobigeon, Nicolas, Cavalcanti, Yanna, Oberlin, Thomas, and Chabert, Marie

Subjects
FOS: Computer and information sciences, Computer Vision and Pattern Recognition (cs.CV), Physics - Data Analysis, Statistics and Probability, Image and Video Processing (eess.IV), FOS: Electrical engineering, electronic engineering, information engineering, Computer Science - Computer Vision and Pattern Recognition, FOS: Physical sciences, Electrical Engineering and Systems Science - Image and Video Processing, Data Analysis, Statistics and Probability (physics.data-an)
Abstract

Archetypal scenarios for change detection generally consider two images acquired through sensors of the same modality. However, in some specific cases such as emergency situations, the only images available may be those acquired through sensors of different modalities. This paper addresses the problem of unsupervisedly detecting changes between two observed images acquired by sensors of different modalities with possibly different resolutions. These sensor dissimilarities introduce additional issues in the context of operational change detection that are not addressed by most of the classical methods. This paper introduces a novel framework to effectively exploit the available information by modelling the two observed images as a sparse linear combination of atoms belonging to a pair of coupled overcomplete dictionaries learnt from each observed image. As they cover the same geographical location, codes are expected to be globally similar, except for possible changes in sparse spatial locations. Thus, the change detection task is envisioned through a dual code estimation which enforces spatial sparsity in the difference between the estimated codes associated with each image. This problem is formulated as an inverse problem which is iteratively solved using an efficient proximal alternating minimization algorithm accounting for nonsmooth and nonconvex functions. The proposed method is applied to real images with simulated yet realistic and real changes. A comparison with state-of-the-art change detection methods evidences the accuracy of the proposed strategy., Submitted manuscript under consideration at Computer Vision and Image Understanding

Published
2018

34. Asymptotically Exact Data Augmentation: Models, Properties, and Algorithms.

Author

Vono, Maxime, Dobigeon, Nicolas, and Chainais, Pierre

Subjects
*DATA augmentation, *DATA modeling, *MARKOV chain Monte Carlo
Abstract

Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain Monte Carlo ones. Nonetheless, introducing appropriate auxiliary variables while preserving the initial target probability distribution and offering a computationally efficient inference cannot be conducted in a systematic way. To deal with such issues, this article studies a unified framework, coined asymptotically exact data augmentation (AXDA), which encompasses both well-established and more recent approximate augmented models. In a broader perspective, this article shows that AXDA models can benefit from interesting statistical properties and yield efficient inference algorithms. In non-asymptotic settings, the quality of the proposed approximation is assessed with several theoretical results. The latter are illustrated on standard statistical problems. including computer code for this article are available online. [ABSTRACT FROM AUTHOR]

Published
2021
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35. Bayesian nonparametric Principal Component Analysis

Author

Elvira, Clément, Chainais, Pierre, Dobigeon, Nicolas, Centrale Lille, Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Institut National Polytechnique (Toulouse) (Toulouse INP), ANR-13-BS03-0006,BNPSI,Méthodes bayésiennes non paramétriques pour le traitement du signal et de l'image(2013), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
FOS: Computer and information sciences, Bayesian nonparametrics, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, dimension reduction, Statistics - Machine Learning, Machine Learning (stat.ML), Indian buffet process, distribution on the Stiefel manifold, distribution on the Stiefel man- ifold
Abstract

Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works have proposed a probabilistic approach able to infer the number of significant components. To this purpose, this paper introduces a Bayesian nonparametric principal component analysis (BNP-PCA). The proposed model projects observations onto a random orthogonal basis which is assigned a prior distribution defined on the Stiefel manifold. The prior on factor scores involves an Indian buffet process to model the uncertainty related to the number of components. The parameters of interest as well as the nuisance parameters are finally inferred within a fully Bayesian framework via Monte Carlo sampling. A study of the (in-)consistence of the marginal maximum a posteriori estimator of the latent dimension is carried out. A new estimator of the subspace dimension is proposed. Moreover, for sake of statistical significance, a Kolmogorov-Smirnov test based on the posterior distribution of the principal components is used to refine this estimate. The behaviour of the algorithm is first studied on various synthetic examples. Finally, the proposed BNP dimension reduction approach is shown to be easily yet efficiently coupled with clustering or latent factor models within a unique framework.

Published
2017

36. Ecosystem services assessment using hyperspectral images

Author

Fauvel, Mathieu, Uezato, Tatsumi, Duflot, Rémi, Dobigeon, Nicolas, Vialatte, Aude, Sheeren, David, Dynamiques Forestières dans l'Espace Rural (DYNAFOR), Institut National de la Recherche Agronomique (INRA)-École nationale supérieure agronomique de Toulouse [ENSAT]-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Dynamiques et écologie des paysages agriforestiers (DYNAFOR), École nationale supérieure agronomique de Toulouse [ENSAT]-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Biodiversité agroécologie et aménagement du paysage (UMR BAGAP), Institut National de la Recherche Agronomique (INRA)-AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Ecole supérieure d'Agricultures d'Angers (ESA), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Institut National de la Recherche Agronomique (INRA)-AGROCAMPUS OUEST-Ecole supérieure d'Agricultures d'Angers (ESA), and ProdInra, Migration

Subjects
[SDV] Life Sciences [q-bio], [SDV]Life Sciences [q-bio], [SHS] Humanities and Social Sciences, ComputingMilieux_MISCELLANEOUS, [SHS]Humanities and Social Sciences
Abstract

International audience

Published
2017

37. A Bayesian model for joint unmixing, clustering and classification of hyperspectral data

Author

Lagrange, Adrien, Dobigeon, Nicolas, Fauvel, Mathieu, May, Stéphane, Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, Dynamiques Forestières dans l'Espace Rural (DYNAFOR), Institut National de la Recherche Agronomique (INRA)-Ecole Nationale Supérieure Agronomique de Toulouse-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Centre National d'Études Spatiales [Toulouse] (CNES), Ecole Nationale Supérieure d'Electrotechnique, d'Electronique, d'Informatique, d'Hydraulique et de Télécommunications, Institut National de la Recherche Agronomique (INRA)-École nationale supérieure agronomique de Toulouse [ENSAT]-Institut National Polytechnique (Toulouse) (Toulouse INP), Centre National d'Études Spatiales - CNES (FRANCE), Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - INPT (FRANCE), Institut National de la Recherche Agronomique - INRA (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Signal et Communications (IRIT-SC), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Institut National Polytechnique (Toulouse) (Toulouse INP), (OATAO), Open Archive Toulouse Archive Ouverte, and Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)

Subjects
Traitement des images, ComputingMethodologies_PATTERNRECOGNITION, Markov random field, Image interpretation, [INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], [SDV]Life Sciences [q-bio], Bayesian model, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Super- Vised learning, [SHS]Humanities and Social Sciences
Abstract

International audience; Supervised classification and spectral unmixing are two methods to extract information from hyperspectral images. However, despite their complementarity, they have been scarcely considered jointly. This paper presents a new hierarchical Bayesian model to perform simultaneously both analysis in order to ensure that they benefit from each other. A linear mixture model is proposed to described the pixel measurements. Then a clustering is performed to identify groups of statistically similar abundance vectors. A Markov random field (MRF) is used as prior for the corresponding cluster labels. It pro-motes a spatial regularization through a Potts-Markov potential and also includes a local potential induced by the classification. Finally, the classification exploits a set of possibly corrupted labeled data provided by the end-user. Model parameters are estimated thanks to a Markov chain Monte Carlo (MCMC) algorithm. The interest of the proposed model is illustrated on synthetic and real data.

Published
2017

38. A Bayesian model for joint unmixing, clustering and classification of hyperspectral data

Author

Dobigeon , Nicolas, Fauvel, Mathieu, May, Stéphane, and Lagrange, Adrien

Subjects
bayesian model, markov random field, super- vised learning, image interpretation, ComputingMethodologies_PATTERNRECOGNITION
Abstract

Supervised classification and spectral unmixing are two methods to extract information from hyperspectral images. However, despite their complementarity, they have been scarcely considered jointly. This paper presents a new hierarchical Bayesian model to perform simultaneously both analysis in order to ensure that they benefit from each other. A linear mixture model is proposed to described the pixel measurements. Then a clustering is performed to identify groups of statistically similar abundance vectors. A Markov random field (MRF) is used as prior for the corresponding cluster labels. It pro-motes a spatial regularization through a Potts-Markov potential and also includes a local potential induced by the classification. Finally, the classification exploits a set of possibly corrupted labeled data provided by the end-user. Model parameters are estimated thanks to a Markov chain Monte Carlo (MCMC) algorithm. The interest of the proposed model is illustrated on synthetic and real data.

Published
2017

39. Bayesian-driven criterion to automatically select the regularization parameter in the l1-Potts model

Author

Frecon, Jordan, Pustelnik, Nelly, Dobigeon, Nicolas, Wendt, Herwig, Abry, Patrice, Centre National de la Recherche Scientifique - CNRS (FRANCE), Ecole Normale Supérieure de Lyon - ENS de Lyon (FRANCE), Institut National Polytechnique de Toulouse - INPT (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Université Claude Bernard-Lyon I - UCBL (FRANCE), Université de Lyon - UDL (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Institut National Polytechnique (Toulouse) (Toulouse INP), Centre National de la Recherche Scientifique (CNRS), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
[INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Vision par ordinateur et reconnaissance de formes, Laplacian noise, Intelligence artificielle, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Traitement des images, Regularization parameter automated selection, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Hierarchical Bayesian model, Traitement du signal et de l'image, Potts model, Piecewise constant denoising, Synthèse d'image et réalité virtuelle
Abstract

International audience; This contribution focuses, within the ℓ1-Potts model, on the automated estimation of the regularization parameter balancing the ℓ1 data fidelity term and the TVℓ0 penalization. Variational approaches based on total variation gained considerable interest to solve piecewise constant denoising problems thanks to their deterministic setting and low computational cost. However, the quality of the achieved solution strongly depends on the tuning of the regularization parameter. While recent works have tailored various hierarchical Bayesian procedures to additionally estimate the regularization parameter for Gaussian noise, less attention has been granted to Laplacian noise, of interested in numerous applications. This contribution promotes a fast and parameter-free denoising procedure for piecewise constant signals corrupted by Laplacian noise, that includes automated selection of the regularization parameter. It relies on the minimization of a Bayesian-driven criterion whose similarities with the ℓ1-Potts model permit to derive a computationally efficient algorithm.

Published
2017

40. Matrix Cofactorization for Joint Spatial–Spectral Unmixing of Hyperspectral Images.

Author

Lagrange, Adrien, Fauvel, Mathieu, May, Stephane, and Dobigeon, Nicolas

Subjects
MATRIX decomposition, TIKHONOV regularization, MATRICES (Mathematics), AMBIGUITY, IMAGE, EVALUATION methodology, TASK analysis
Abstract

Hyperspectral unmixing aims at identifying a set of elementary spectra and the corresponding mixture coefficients for each pixel of an image. As the elementary spectra correspond to the reflectance spectra of real materials, they are often very correlated, thus yielding an ill-conditioned problem. To enrich the model and reduce ambiguity due to the high correlation, it is common to introduce spatial information to complement the spectral information. The most common way to introduce spatial information is to rely on a spatial regularization of the abundance maps. In this article, instead of considering a simple but limited regularization process, spatial information is directly incorporated through the newly proposed context of spatial unmixing. Contextual features are extracted for each pixel, and this additional set of observations is decomposed according to a linear model. Finally, the spatial and spectral observations are unmixed jointly through a cofactorization model. In particular, this model introduces a coupling term used to identify clusters of shared spatial and spectral signatures. An evaluation of the proposed method is conducted on synthetic and real data and shows that results are accurate and also very meaningful since they describe both spatially and spectrally the various areas of the scene. [ABSTRACT FROM AUTHOR]

Published
2020
Full Text
View/download PDF

42. Fast Single Image Super-Resolution Using a New Analytical Solution for l2–l2 Problems

Author

Zhao, Ningning, Wei, Qi, Basarab, Adrian, Dobigeon, Nicolas, Kouamé, Denis, Tourneret, Jean-Yves, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), University of Cambridge (UNITED KINGDOM), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Institut National Polytechnique de Toulouse - INPT (FRANCE), Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Traitement et Compréhension d’Images (IRIT-TCI), University of Cambridge [UK] (CAM), Université Toulouse III - Paul Sabatier (UT3), Institut National Polytechnique (Toulouse) (Toulouse INP), and CoMputational imagINg anD viSion (IRIT-MINDS)

Subjects
Traitement des images, Variable splitting based algorithms, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Decimation, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], Algorithme et structure de données, Single image super-resolution, Deconvolution, Block circulant matrix
Abstract

International audience; This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high- resolution image from its blurred, decimated, and noisy version. The existing algorithms for single image SR use different strate- gies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution is derived and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an l2 -regularized quadratic model, i.e., an l2 –l2 optimization problem. The flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded into traditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with existing techniques.

Published
2016

43. Fast Single Image Super-Resolution

Author

Zhao, Ningning, Wei, Qi, Basarab, Adrian, Dobigeon, Nicolas, Kouame, Denis, and Tourneret, Jean-Yves

Subjects
FOS: Computer and information sciences, Computer Vision and Pattern Recognition (cs.CV), Computer Science - Computer Vision and Pattern Recognition
Abstract

This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high resolution image from its blurred, decimated and noisy version. The existing algorithms for single image SR use different strategies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution can be obtained and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an $\ell_2$-regularized quadratic model, i.e., an $\ell_2$-$\ell_2$ optimization problem. Furthermore, the flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded intotraditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with the existing techniques.

Published
2015

44. Hyperspectral Pansharpening: A Review

Author

Loncan, Laetitia, Almeida, Luís, Bioucas-Dias, José, Briottet, Xavier, Chanussot, Jocelyn, Dobigeon, Nicolas, Fabre, Sophie, Liao, Wenzhi, Licciardi, Giorgio A., Simões, Miguel, Tourneret, Jean-Yves, Veganzones, Miguel Angel, Vivone, Gemine, Wei, Qi, Yokoya, Naoto, ONERA / DOTA, Université de Toulouse [Toulouse], ONERA-PRES Université de Toulouse, GIPSA - Signal Images Physique (GIPSA-SIGMAPHY), Département Images et Signal (GIPSA-DIS), Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Instituto de Telecomunicações [Lisboa, Portugal], Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Institut National Polytechnique (Toulouse) (Toulouse INP), Universiteit Gent = Ghent University [Belgium] (UGENT), CoMputational imagINg anD viSion (IRIT-MINDS), North Atlantic Treaty Organization (NATO) Science and Technology Organization (STO) Centre for Maritime Research and Experimentation (CMRE), and The University of Tokyo (UTokyo)

Subjects
[SPI]Engineering Sciences [physics], [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Hyperspectral Image, Image fusion, Pansharpening
Abstract

oatao 14340; International audience; Pansharpening aims at fusing a panchromatic image with a multispectral one, to generate an image with the high spatial resolution of the former and the high spectral resolution of the latter. In the last decade, many algorithms have been presented in the literature for pansharpening using multispectral data. With the increasing availability of hyperspectral systems, these methods are now being adapted to hyperspectral images. In this work, we compare new pansharpening techniques designed for hyperspectral data with some of the state of the art methods for multispectral pansharpening, which have been adapted for hyperspectral data. Eleven methods from different classes (component substitution, multiresolution analysis, hybrid, Bayesian and matrix factorization) are analyzed. These methods are applied to three datasets and their effectiveness and robustness are evaluated with widely used performance indicators. In addition, all the pansharpening techniques considered in this paper have been implemented in a MATLAB toolbox that is made available to the community.; Pansharpening aims at fusing a panchromatic image with a multispectral one, to generate an image with the high spatial resolution of the former and the high spectral resolution of the latter. In the last decade, many algorithms have been presented in the literature for pansharpening using multispectral data. With the increasing availability of hyperspectral systems, these methods are now being adapted to hyperspectral images. In this work, we compare new pansharpening techniques designed for hyperspectral data with some of the state of the art methods for multispectral pansharpening, which have been adapted for hyperspectral data. Eleven methods from different classes (component substitution, multiresolution analysis, hybrid, Bayesian and matrix factorization) are analyzed. These methods are applied to three datasets and their effectiveness and robustness are evaluated with widely used performance indicators. In addition, all the pansharpening techniques considered in this paper have been implemented in a MATLAB toolbox that is made availableto the community.

Published
2015

45. Estimation bayésienne locale du paramètre de multifractalité à l'aide d'un algorithme de Monte Carlo Hamiltonien

Author

Combrexelle, Sébastien, Wendt, Herwig, Tourneret, Jean-Yves, Dobigeon, Nicolas, Mc Laughlin, Stephen, Abry, Patrice, Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), CoMputational imagINg anD viSion (IRIT-MINDS), Institut National Polytechnique (Toulouse) (Toulouse INP), Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Centre National de la Recherche Scientifique - CNRS (FRANCE), Ecole Normale Supérieure de Lyon - ENS de Lyon (FRANCE), Institut National Polytechnique de Toulouse - INPT (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), and Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)

Subjects
Traitement des images, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Traitement du signal et de l'image, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Vision par ordinateur et reconnaissance de formes, Représentations et modèles, Intelligence artificielle, Synthèse d'image et réalité virtuelle, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

International audience; La caractérisation de la texture d’une image peut être conduite via l’étude des fluctuations de la régularité locale de son amplitude dans le cadre théorique de l’analyse multifractale. Les images étant souvent composées de différentes textures, cette analyse doit être locale. Cet article s’attaque à ce problème en formulant un modèle bayésien par patch reposant sur un modèle semi-paramétrique récemment proposé pour la statistique du logarithme des coefficients dominants. Les estimateurs bayésiens sont obtenus via une procédure d’échantillonnage utilisant un algorithme de Monte-Carlo Hamiltonien. Les performances de ces estimateurs sont illustrées à l’aide de processus synthétiques.

Published
2015

46. Non‐linear unmixing of hyperspectral images using multiple‐kernel self‐organising maps.

Author

Rashwan, Shaheera, Dobigeon, Nicolas, Sheta, Walaa, and Hassan, Hanan

Abstract

The spatial pixel resolution of common multispectral and hyperspectral sensors is generally not sufficient to avoid that multiple elementary materials contribute to the observed spectrum of a single pixel. To alleviate this limitation, spectral unmixing is a by‐pass procedure which consists in decomposing the observed spectra associated with these mixed pixels into a set of component spectra, or endmembers, and a set of corresponding proportions, or abundances, that represent the proportion of each endmember in these pixels. In this study, a spectral unmixing technique is proposed to handle the challenging scenario of non‐linear mixtures. This algorithm relies on a dedicated implementation of multiple‐kernel learning using self‐organising map proposed as a solver for the non‐linear unmixing problem. Based on a priori knowledge of the endmember spectra, it aims at estimating their relative abundances without specifying the non‐linear model under consideration. It is compared to state‐of‐the‐art algorithms using synthetic yet realistic and real hyperspectral images. Results obtained from experiments conducted on synthetic and real hyperspectral images assess the potential and the effectiveness of this unmixing strategy. Finally, the relevance and potential parallel implementation of the proposed method is demonstrated. [ABSTRACT FROM AUTHOR]

Published
2019
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47. Factor Analysis of Dynamic PET Images: Beyond Gaussian Noise.

Author

Cavalcanti, Yanna Cruz, Oberlin, Thomas, Dobigeon, Nicolas, Fevotte, Cedric, Stute, Simon, Ribeiro, Maria-Joao, and Tauber, Clovis

Subjects
IMAGE denoising, RANDOM noise theory, POSITRON emission tomography, FACTOR analysis, NONNEGATIVE matrices, MATRIX decomposition
Abstract

Factor analysis has proven to be a relevant tool for extracting tissue time-activity curves (TACs) in dynamic PET images, since it allows for an unsupervised analysis of the data. Reliable and interpretable results are possible only if it is considered with respect to suitable noise statistics. However, the noise in reconstructed dynamic PET images is very difficult to characterize, despite the Poissonian nature of the count rates. Rather than explicitly modeling the noise distribution, this paper proposes to study the relevance of several divergence measures to be used within a factor analysis framework. To this end, the $\beta $ -divergence, widely used in other applicative domains, is considered to design the data-fitting term involved in three different factor models. The performances of the resulting algorithms are evaluated for different values of $\beta $ , in a range covering Gaussian, Poissonian, and Gamma-distributed noises. The results obtained on two different types of synthetic images and one real image show the interest of applying non-standard values of $\beta $ to improve the factor analysis. [ABSTRACT FROM AUTHOR]

Published
2019
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48. Hyperspectral Unmixing With Spectral Variability Using Adaptive Bundles and Double Sparsity.

Author

Uezato, Tatsumi, Fauvel, Mathieu, and Dobigeon, Nicolas

Subjects
PIXELS, DISTRIBUTION (Probability theory), DATA mining
Abstract

Spectral variability is one of the major issues when conducting hyperspectral unmixing. Within a given image composed of some elementary materials (herein referred to as endmember classes), the spectral signatures characterizing these classes may spatially vary due to intrinsic component fluctuations or external factors (illumination). These redundant multiple endmember spectra within each class adversely affect the performance of unmixing methods. This paper proposes a mixing model that explicitly incorporates a hierarchical structure of redundant multiple spectra representing each class. The proposed method is designed to promote sparsity on the selection of both spectra and classes within each pixel. The resulting unmixing algorithm is able to adaptively recover several bundles of endmember spectra associated with each class and robustly estimate abundances. In addition, its flexibility allows a variable number of classes to be present within each pixel of the hyperspectral image to be unmixed. The proposed method is compared with other state-of-the-art unmixing methods that incorporate sparsity using both simulated and real hyperspectral data. The results show that the proposed method can successfully determine the variable number of classes present within each class and estimate the corresponding class abundances. [ABSTRACT FROM AUTHOR]

Published
2019
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49. Partially Asynchronous Distributed Unmixing of Hyperspectral Images.

Author

Thouvenin, Pierre-Antoine, Dobigeon, Nicolas, and Tourneret, Jean-Yves

Subjects
*HYPERSPECTRAL imaging systems, *IMAGE processing, *SIMULATION methods & models, *REMOTE sensing, *SIGNAL processing
Abstract

So far, the problem of unmixing large or multitemporal hyperspectral data sets has been specifically addressed in the remote sensing literature only by a few dedicated strategies. Among them, some attempts have been made within a distributed estimation framework, in particular, relying on the alternating direction method of multipliers. In this paper, we propose to study the interest of a partially asynchronous distributed unmixing procedure based on a recently proposed asynchronous algorithm. Under standard assumptions, the proposed algorithm inherits its convergence properties from recent contributions in nonconvex optimization, while allowing the problem of interest to be efficiently addressed. Comparisons with a distributed synchronous counterpart of the proposed unmixing procedure allow its interest to be assessed on synthetic and real data. Besides, thanks to its genericity and flexibility, the procedure investigated in this paper can be implemented to address various matrix factorization problems. [ABSTRACT FROM AUTHOR]

Published
2019
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50. Learning a fast transform with a dictionary

Author

Chabiron, Olivier, Malgouyres, François, Tourneret, Jean-Yves, Dobigeon, Nicolas, Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Télécommunications Spatiales et Aéronautiques - Telecommunications for Space ant Aeronautics (TéSA), Laboratoire de recherche coopératif dans les télécommunications spatiales et aéronautiques (TESA), Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - INPT (FRANCE), Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), CoMputational imagINg anD viSion (IRIT-MINDS), Institut National Polytechnique (Toulouse) (Toulouse INP), ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), and Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)

Subjects
Gauss-Seidel algorithm, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Vision par ordinateur et reconnaissance de formes, Intelligence artificielle, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Traitement des images, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Computer Science::Computer Vision and Pattern Recognition, Dictionnary learning, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Traitement du signal et de l'image, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Synthèse d'image et réalité virtuelle
Abstract

International audience; — A powerful approach to sparse representation, dictionary learning consists in finding a redundant frame in which the representation of a particular class of images is sparse. In practice, all algorithms performing dictionary learning iteratively estimate the dictionary and a sparse representation of the images using this dictionary. However, the numerical complexity of dictionary learning restricts its use to atoms with a small support. A way to alleviate these issues is introduced in this paper, consisting in dictionary atoms obtained by translating the composition of K convolutions with S-sparse kernels of known support. The dictionary update step associated with this strategy is a non-convex optimization problem, which we study here. A block-coordinate descent or Gauss-Seidel algorithm is proposed to solve this problem, whose search space is of dimension KS, which is much smaller than the size of the image. Moreover, the complexity of the algorithm is linear with respect to the size of the image, allowing larger atoms to be learned (as opposed to small patches). An experiment is presented that shows the approximation of a large cosine atom with K = 7 sparse kernels, demonstrating a very good accuracy.

Published
2014

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