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In the context of Earth observation, change detection boils down to comparing images acquired at different times by sensors of possibly different spatial and/or spectral resolutions or different modalities (e.g., optical or radar). Even when considering only optical images, this task has proven to be challenging as soon as the sensors differ by their spatial and/or spectral resolutions. This paper proposes a novel unsupervised change detection method dedicated to images acquired by such so-called heterogeneous optical sensors. It capitalizes on recent advances which formulate the change detection task into a robust fusion framework. Adopting this formulation, the work reported in this paper shows that any off-the-shelf network trained beforehand to fuse optical images of different spatial and/or spectral resolutions can be easily complemented with a network of the same architecture and embedded into an adversarial framework to perform change detection. A comparison with state-of-the-art change detection methods demonstrates the versatility and the effectiveness of the proposed approach. • Detecting changes between images acquired by heterogeneous sensors is formulated as a robust fusion problem. • The method is able to handle multi-band images with possibly different spatial and/or spectral resolutions. • The method is unsupervised, i.e., it does not need a train set composed of image pairs with associated binary change maps. • Any pretrained deep network designed to fuse heterogeneous images can be reused to perform change detection. • When compared to conventional approaches, the strategy appears to be more flexible while competing favorably. [ABSTRACT FROM AUTHOR]

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]

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]

Unsupervised change detection techniques are generally constrained to two multi-band optical images acquired at different times through sensors sharing the same spatial and spectral resolution. In the case of the optical modality, largely studied in the remote sensing community, a straight comparison of homologous pixels such as pixel-wise differencing is suitable. However, in some specific cases such as emergency situations, punctual missions, defense and security, the only available images may be those acquired through different kinds of sensors with different resolutions. Recently some change detection techniques, dealing with images with different spatial and spectral resolutions, have been proposed. Nevertheless, they are focused on a specific scenario where one image has a high spatial and low spectral resolution while the other has a low spatial and high spectral resolution. This paper addresses the problem of detecting changes between any two multi-band optical images disregarding their spatial and spectral resolution disparities. To overcome resolution disparity, state-of-the art methods apply conventional change detection methods after preprocessing steps applied independently on the two images, e.g. resampling operations intended to reach the same spatial and spectral resolutions. Nevertheless, these preprocessing steps may waste relevant information since they do not take into account the strong interplay existing between the two images. Conversely, in this paper, we propose a method that more effectively uses the available information by modeling the two observed images as spatially and spectrally degraded versions of two (unobserved) latent images characterized by the same high spatial and high spectral resolutions. Covering the same scene, the latent images are expected to be globally similar except for possible changes in spatially sparse locations. Thus, the change detection task is envisioned through a robust fusion task which enforces the differences between the estimated latent images to be spatially sparse. We show that this robust fusion can be formulated as an inverse problem which is iteratively solved using an alternating minimization strategy. The proposed framework is implemented for an exhaustive list of applicative scenarios and applied to real multi-band optical images. A comparison with state-of-the-art change detection methods evidences the accuracy and the versatility of the proposed robust fusion-based strategy. • Detecting changes between two optical images is formulated as a robust fusion. • The proposed method handles all combination of spatial and spectral image resolutions. • Robust fusion is performed using an alternating minimization algorithm. • All steps of the algorithm boil down to conducting a standard image processing task. • The performance is assessed on a comprehensive set of experiments. [ABSTRACT FROM AUTHOR]

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]

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]

Hyperspectral unmixing is aimed at identifying the reference spectral signatures composing a hyperspectral image and their relative abundance fractions in each pixel. In practice, the identified signatures may vary spectrally from an image to another due to varying acquisition conditions, thus inducing possibly significant estimation errors. Against this background, the hyperspectral unmixing of several images acquired over the same area is of considerable interest. Indeed, such an analysis enables the endmembers of the scene to be tracked and the corresponding endmember variability to be characterized. Sequential endmember estimation from a set of hyperspectral images is expected to provide improved performance when compared with methods analyzing the images independently. However, the significant size of the hyperspectral data precludes the use of batch procedures to jointly estimate the mixture parameters of a sequence of hyperspectral images. Provided that each elementary component is present in at least one image of the sequence, we propose to perform an online hyperspectral unmixing accounting for temporal endmember variability. The online hyperspectral unmixing is formulated as a two-stage stochastic program, which can be solved using a stochastic approximation. The performance of the proposed method is evaluated on synthetic and real data. Finally, a comparison with independent unmixing algorithms illustrates the interest of the proposed strategy. [ABSTRACT FROM PUBLISHER]

This paper presents a new strategy to correct the Earth data corrupted by spurious samples that are randomly included in the multiplexed data stream provided by the MADRAS instrument. The proposed strategy relies on the construction of a trellis associated with each scan of the multichannel image, modeling the possible occurrences of these erroneous data. A specific weight that promotes the smooth behavior of the signals recorded in each channel is assigned to each transition between trellis states. The joint detection and correction of the erroneous data are conducted using a dynamic programming algorithm for minimizing the overall cost function throughout the trellis. Simulation results obtained on synthetic and real MADRAS data demonstrate the effectiveness of the proposed solution. [ABSTRACT FROM AUTHOR]

Given a mixed hyperspectral data set, linear unmixing aims at estimating the reference spectral signatures composing the data—referred to as endmembers—their abundance fractions and their number. In practice, the identified endmembers can vary spectrally within a given image and can thus be construed as variable instances of reference endmembers. Ignoring this variability induces estimation errors that are propagated into the unmixing procedure. To address this issue, endmember variability estimation consists of estimating the reference spectral signatures from which the estimated endmembers have been derived as well as their variability with respect to these references. This paper introduces a new linear mixing model that explicitly accounts for spatial and spectral endmember variabilities. The parameters of this model can be estimated using an optimization algorithm based on the alternating direction method of multipliers. The performance of the proposed unmixing method is evaluated on synthetic and real data. A comparison with state-of-the-art algorithms designed to model and estimate endmember variability allows the interest of the proposed unmixing solution to be appreciated. [ABSTRACT FROM AUTHOR]

We introduce a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. The new model extends the commonly used linear mixing model by introducing an additional term accounting for possible nonlinear effects, that are treated as sparsely distributed additive outliers. With the standard nonnegativity and sum-to-one constraints inherent to spectral unmixing, our model leads to a new form of robust nonnegative matrix factorization with a group-sparse outlier term. The factorization is posed as an optimization problem, which is addressed with a block-coordinate descent algorithm involving majorization–minimization updates. Simulation results obtained on synthetic and real data show that the proposed strategy competes with the state-of-the-art linear and nonlinear unmixing methods. [ABSTRACT FROM AUTHOR]

Abstract: We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM). [Copyright &y& Elsevier]

Background: This paper introduces a new constrained model and the corresponding algorithm, called unsupervised Bayesian linear unmixing (uBLU), to identify biological signatures from high dimensional assays like gene expression microarrays. The basis for uBLU is a Bayesian model for the data samples which are represented as an additive mixture of random positive gene signatures, called factors, with random positive mixing coefficients, called factor scores, that specify the relative contribution of each signature to a specific sample. The particularity of the proposed method is that uBLU constrains the factor loadings to be non-negative and the factor scores to be probability distributions over the factors. Furthermore, it also provides estimates of the number of factors. A Gibbs sampling strategy is adopted here to generate random samples according to the posterior distribution of the factors, factor scores, and number of factors. These samples are then used to estimate all the unknown parameters. Results: Firstly, the proposed uBLU method is applied to several simulated datasets with known ground truth and compared with previous factor decomposition methods, such as principal component analysis (PCA), non negative matrix factorization (NMF), Bayesian factor regression modeling (BFRM), and the gradient-based algorithm for general matrix factorization (GB-GMF). Secondly, we illustrate the application of uBLU on a real time-evolving gene expression dataset from a recent viral challenge study in which individuals have been inoculated with influenza A/H3N2/Wisconsin. We show that the uBLU method significantly outperforms the other methods on the simulated and real data sets considered here. Conclusions: The results obtained on synthetic and real data illustrate the accuracy of the proposed uBLU method when compared to other factor decomposition methods from the literature (PCA, NMF, BFRM, and GB-GMF). The uBLU method identifies an inflammatory component closely associated with clinical symptom scores collected during the study. Using a constrained model allows recovery of all the inflammatory genes in a single factor. [ABSTRACT FROM AUTHOR]

This paper studies a nonlinear mixing model for hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated by polynomials leading to a polynomial post-nonlinear mixing model. We have shown in a previous paper that the parameters involved in the resulting model can be estimated using least squares methods. A generalized likelihood ratio test based on the estimator of the nonlinearity parameter is proposed to decide whether a pixel of the image results from the commonly used linear mixing model or from a more general nonlinear mixing model. To compute the test statistic associated with the nonlinearity detection, we propose to approximate the variance of the estimated nonlinearity parameter by its constrained Cramér–Rao bound. The performance of the detection strategy is evaluated via simulations conducted on synthetic and real data. More precisely, synthetic data have been generated according to the standard linear mixing model and three nonlinear models from the literature. The real data investigated in this study are extracted from the Cuprite image, which shows that some minerals seem to be nonlinearly mixed in this image. Finally, it is interesting to note that the estimated abundance maps obtained with the post-nonlinear mixing model are in good agreement with results obtained in previous studies. [ABSTRACT FROM PUBLISHER]

Abstract: Recent advances in detectors and computer science have enabled the acquisition and the processing of multidimensional datasets, in particular in the field of spectral imaging. Benefiting from these new developments, Earth scientists try to recover the reflectance spectra of macroscopic materials (e.g., water, grass, mineral types…) present in an observed scene and to estimate their respective proportions in each mixed pixel of the acquired image. This task is usually referred to as spectral mixture analysis or spectral unmixing (SU). SU aims at decomposing the measured pixel spectrum into a collection of constituent spectra, called endmembers, and a set of corresponding fractions (abundances) that indicate the proportion of each endmember present in the pixel. Similarly, when processing spectrum-images, microscopists usually try to map elemental, physical and chemical state information of a given material. This paper reports how a SU algorithm dedicated to remote sensing hyperspectral images can be successfully applied to analyze spectrum-image resulting from electron energy-loss spectroscopy (EELS). SU generally overcomes standard limitations inherent to other multivariate statistical analysis methods, such as principal component analysis (PCA) or independent component analysis (ICA), that have been previously used to analyze EELS maps. Indeed, ICA and PCA may perform poorly for linear spectral mixture analysis due to the strong dependence between the abundances of the different materials. One example is presented here to demonstrate the potential of this technique for EELS analysis. [Copyright &y& Elsevier]

This paper addresses the problem of jointly estimating the statistical distribution and segmenting lesions in multiple-tissue high-frequency skin ultrasound images. The distribution of multiple-tissue images is modeled as a spatially coherent finite mixture of heavy-tailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by enforcing local dependence between the mixture components. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a label-vector associating each voxel to a tissue. More precisely, a hybrid Metropolis-within-Gibbs sampler is used to draw samples that are asymptotically distributed according to the posterior distribution of the Bayesian model. The Bayesian estimators of the model parameters are then computed from the generated samples. Simulation results are conducted on synthetic data to illustrate the performance of the proposed estimation strategy. The method is then successfully applied to the segmentation of in vivo skin tumors in high-frequency 2-D and 3-D ultrasound images. [ABSTRACT FROM PUBLISHER]

In numerous applications, it is required to estimate the principal subspace of the data, possibly from a very limited number of samples. Additionally, it often occurs that some rough knowledge about this subspace is available and could be used to improve subspace estimation accuracy in this case. This is the problem we address herein and, in order to solve it, a Bayesian approach is proposed. The main idea consists of using the CS decomposition of the semi-orthogonal matrix whose columns span the subspace of interest. This parametrization is intuitively appealing and allows for non informative prior distributions of the matrices involved in the CS decomposition and very mild assumptions about the angles between the actual subspace and the prior subspace. The posterior distributions are derived and a Gibbs sampling scheme is presented to obtain the minimum mean-square distance estimator of the subspace of interest. Numerical simulations and an application to real hyperspectral data assess the validity and the performances of the estimator. [ABSTRACT FROM PUBLISHER]

This paper is concerned with joint Bayesian endmember extraction and linear unmixing of hyperspectral images using a spatial prior on the abundance vectors. We propose a generative model for hyperspectral images in which the abundances are sampled from a Dirichlet distribution (DD) mixture model, whose parameters depend on a latent label process. The label process is then used to enforces a spatial prior which encourages adjacent pixels to have the same label. A Gibbs sampling framework is used to generate samples from the posterior distributions of the abundances and the parameters of the DD mixture model. The spatial prior that is used is a tree-structured sticky hierarchical Dirichlet process (SHDP) and, when used to determine the posterior endmember and abundance distributions, results in a new unmixing algorithm called spatially constrained unmixing (SCU). The directed Markov model facilitates the use of scale-recursive estimation algorithms, and is therefore more computationally efficient as compared to standard Markov random field (MRF) models. Furthermore, the proposed SCU algorithm estimates the number of regions in the image in an unsupervised fashion. The effectiveness of the proposed SCU algorithm is illustrated using synthetic and real data. [ABSTRACT FROM PUBLISHER]

We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace \mmb U and its estimate \mathhat\mmb U may not be adequate as the MSE is not the natural metric in the Grassmann manifold GN,p, i.e., the set of p-dimensional subspaces in \BBR^N. As an alternative, we propose to carry out subspace estimation by minimizing the mean square distance between \mmb U and its estimate, where the considered distance is a natural metric in the Grassmann manifold, viz. the distance between the projection matrices. We show that the resulting estimator is no longer the posterior mean of \mmb U but entails computing the principal eigenvectors of the posterior mean of \mmbUU^T. Derivation of the minimum mean square distance (MMSD) estimator is carried out in a few illustrative examples including a linear Gaussian model for the data and Bingham or von Mises Fisher prior distributions for \mmb U. In all scenarios, posterior distributions are derived and the MMSD estimator is obtained either analytically or implemented via a Markov chain Monte Carlo simulation method. The method is shown to provide accurate estimates even when the number of samples is lower than the dimension of \mmb U. An application to hyperspectral imagery is finally investigated. [ABSTRACT FROM AUTHOR]

This paper describes a new algorithm for hyperspectral image unmixing. Most unmixing algorithms proposed in the literature do not take into account the possible spatial correlations between the pixels. In this paper, a Bayesian model is introduced to exploit these correlations. The image to be unmixed is assumed to be partitioned into regions (or classes) where the statistical properties of the abundance coefficients are homogeneous. A Markov random field, is then proposed to model the spatial dependencies between the pixels within any class. Conditionally upon a given class, each pixel is modeled by using the classical linear mixing model with additive white Gaussian noise. For this model, the posterior distributions of the unknown parameters and hyperparameters allow the parameters of interest to be inferred. These parameters include the abundances for each pixel, the means and variances of the abundances for each class, as well as a classification map indicating the classes of all pixels in the image. To overcome the complexity of the posterior distribution, we consider a Markov chain Monte Carlo method that generates samples asymptotically distributed according to the posterior. The generated samples are then used for parameter and hyperparameter estimation. The accuracy of the proposed algorithms is illustrated on synthetic and real data. [ABSTRACT FROM AUTHOR]

This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of so-called endmembers. These endmembers are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model endmembers as Gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous N-finder (N-FINDR) or Vertex Component Analysis (VCA) algorithms. This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters. A hybrid Gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances. The performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This undercomplete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a Bayesian framework. First, the unknown sparse sources are modeled as Bernoulli-Gaussian processes. To promote sparsity, a weighted mixture of an atom at zero and a Gaussian distribution is proposed as prior distribution for the unobserved sources. A noninformative prior distribution defined on an appropriate Stiefel manifold is elected for the mixing matrix. The Bayesian inference on the unknown parameters is conducted using a Markov chain Monte Carlo (MCMC) method. A partially collapsed Gibbs sampler is designed to generate samples asymptotically distributed according to the joint posterior distribution of the unknown model parameters and hyperparameters. These samples are then used to approximate the joint maximum a posteriori estimator of the sources and mixing matrix. Simulations conducted on synthetic data are reported to illustrate the performance of the method for recovering sparse representations. An application to sparse coding on undercomplete dictionary is finally investigated. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the problem of separating spectral sources which are linearly mixed with unknown proportions. The main difficulty of the problem is to ensure the full additivity (sum-to-one) of the mixing coefficients and non-negativity of sources and mixing coefficients. A Bayesian estimation approach based on Gamma priors was recently proposed to handle the non-negativity constraints in a linear mixture model. However, incorporating the full additivity constraint requires further developments. This paper studies a new hierarchical Bayesian model appropriate to the non-negativity and sum-to-one constraints associated to the sources and the mixing coefficients of linear mixtures. The estimation of the unknown parameters of this model is performed using samples obtained with an appropriate Gibbs algorithm. The performance of the proposed algorithm is evaluated through simulation results conducted on synthetic mixture data. The proposed approach is also applied to the processing of multicomponent chemical mixtures resulting from Raman spectroscopy. [Copyright &y& Elsevier]

This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical Bayesian model. This model assumes conjugate prior distributions for these parameters, accounts for nonnegativity and fulladditivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution.. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images. [ABSTRACT FROM AUTHOR]

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument. [ABSTRACT FROM AUTHOR]

This paper proposes a hierarchical Bayesian model that can be used for semi-supervised hyperspectral image unmixing. The model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters appearing in this model satisfy positivity and additivity constraints. These constraints are naturally expressed in a Bayesian context by using appropriate abundance prior distributions. The posterior distributions of the unknown model parameters are then derived. A Gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances. An extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library. The performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data. [ABSTRACT FROM PUBLISHER]

We propose a joint segmentation algorithm for piecewise constant autoregressive (AR) processes recorded by several independent sensors. The algorithm is based on a hierarchical Bayesian model. Appropriate priors allow us to introduce correlations between the change locations of the observed signals. Numerical problems inherent to Bayesian inference are solved by a Gibbs sampling strategy. The proposed joint segmentation methodology yields improved segmentation results when compared with parallel and independent individual signal segmentations. The initial algorithm is derived for piecewise constant AR processes whose orders are fixed on each segment. However, an extension to models with unknown model orders is also discussed. Theoretical results are illustrated by many simulations conducted with synthetic signals and real arc-tracking and speech signals. [ABSTRACT FROM AUTHOR]

Astronomy and other sciences often face the problem of detecting and characterizing structure in two or more related time series. This paper approaches such problems using Bayesian priors to represent relationships between signals with various degrees of certainty, and not just rigid constraints. The segmentation is conducted by using a hierarchical Bayesian approach to a piecewise constant Poisson rate model. A Gibbs sampling strategy allows joint estimation of the unknown parameters and hyperparameters. Results obtained with synthetic and real photon counting data illustrate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

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]

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]

Highlights • An enhanced factor analysis of dynamic PET images is proposed, which explicitly models the variability of the specific binding factor time-activity-curve. • The decomposition relies on a new interpretation for the spatial heterogeneity of PET images. • Taking into account the spatial heterogeneity clearly improves the estimation of the specific binding factor and its spatial map. Graphical abstract Abstract To analyze dynamic positron emission tomography (PET) images, various generic multivariate data analysis techniques have been considered in the literature, such as principal component analysis (PCA), independent component analysis (ICA), factor analysis and nonnegative matrix factorization (NMF). Nevertheless, these conventional approaches neglect any possible nonlinear variations in the time activity curves describing the kinetic behavior of tissues with specific binding, which limits their ability to recover a reliable, understandable and interpretable description of the data. This paper proposes an alternative analysis paradigm that accounts for spatial fluctuations in the exchange rate of the tracer between a free compartment and a specifically bound ligand compartment. The method relies on the concept of linear unmixing, usually applied on the hyperspectral domain, which combines NMF with a sum-to-one constraint that ensures an exhaustive description of the mixtures. The spatial variability of the signature corresponding to the specific binding tissue is explicitly modeled through a perturbed component. The performance of the method is assessed on both synthetic and real data and is shown to compete favorably when compared to other conventional analysis methods. [ABSTRACT FROM AUTHOR]

Spectral unmixing (SU) methods incorporating the spatial regularizations have demonstrated increasing interest. Although spatial regularizers that promote smoothness of the abundance maps have been widely used, they may overly smooth these maps and, in particular, may not preserve edges present in the hyperspectral image. Existing unmixing methods usually ignore these edge structures or use edge information derived from the hyperspectral image itself. However, this information may be affected by the large amounts of noise or variations in illumination, leading to erroneous spatial information incorporated into the unmixing procedure. This paper proposes a simple yet powerful SU framework that incorporates external data [i.e. light detection and ranging (LiDAR) data]. The LiDAR measurements can be easily exploited to adjust the standard spatial regularizations applied to the unmixing process. The proposed framework is rigorously evaluated using two simulated data sets and a real hyperspectral image. It is compared with methods that rely on spatial information derived from a hyperspectral image. The results show that the proposed framework can provide better abundance estimates and, more specifically, can significantly improve the abundance estimates for the pixels affected by shadows. [ABSTRACT FROM AUTHOR]

Change detection (CD) is one of the most challenging issues when analyzing remotely sensed images. Comparing several multidate images acquired through the same kind of sensor is the most common scenario. Conversely, designing robust, flexible, and scalable algorithms for CD becomes even more challenging when the images have been acquired by two different kinds of sensors. This situation arises in the case of emergency under critical constraints. This paper presents, to the best of our knowledge, the first strategy to deal with optical images characterized by dissimilar spatial and spectral resolutions. Typical considered scenarios include CD between panchromatic, multispectral, and hyperspectral images. The proposed strategy consists of a three-step procedure: 1) inferring a high spatial and spectral resolution image by fusion of the two observed images characterized one by a low spatial resolution and the other by a low spectral resolution; 2) predicting two images with, respectively, the same spatial and spectral resolutions as the observed images by the degradation of the fused one; and 3) implementing a decision rule to each pair of observed and predicted images characterized by the same spatial and spectral resolutions to identify changes. To quantitatively assess the performance of the method, an experimental protocol is specifically designed, relying on synthetic yet physically plausible change rules applied to real images. The accuracy of the proposed framework is finally illustrated on real images. [ABSTRACT FROM AUTHOR]

Piecewise constant denoising can be solved either by deterministic optimization approaches, based on the Potts model, or by stochastic Bayesian procedures. The former lead to low computational time but require the selection of a regularization parameter, whose value significantly impacts the achieved solution, and whose automated selection remains an involved and challenging problem. Conversely, fully Bayesian formalisms encapsulate the regularization parameter selection into hierarchical models, at the price of high computational costs. This contribution proposes an operational strategy that combines hierarchical Bayesian and Potts model formulations, with the double aim of automatically tuning the regularization parameter and maintaining computational efficiency. The proposed procedure relies on formally connecting a Bayesian framework to a $\ell _2$ -Potts functional. Behaviors and performance for the proposed piecewise constant denoising and regularization parameter tuning techniques are studied qualitatively and assessed quantitatively, and shown to compare favorably against those of a fully Bayesian hierarchical procedure, both in accuracy and computational load. [ABSTRACT FROM PUBLISHER]

Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients exhibits relevant properties in various applications such as robust encoding in digital communications. Antisparse regularization can be naturally expressed through an \ell \infty -norm penalty. This paper derives a probabilistic formulation of such representations. A new probability distribution, referred to as the democratic prior, is first introduced. Its main properties as well as three random variate generators for this distribution are derived. Then this probability distribution is used as a prior to promote antisparsity in a Gaussian linear model, yielding a fully Bayesian formulation of antisparse coding. Two Markov chain Monte Carlo algorithms are proposed to generate samples according to the posterior distribution. The first one is a standard Gibbs sampler. The second one uses Metropolis–Hastings moves that exploit the proximity mapping of the log-posterior distribution. These samples are used to approximate maximum a posteriori and minimum mean square error estimators of both parameters and hyperparameters. Simulations on synthetic data illustrate the performances of the two proposed samplers, for both complete and over-complete dictionaries. All results are compared to the recent deterministic variational FITRA algorithm. [ABSTRACT FROM PUBLISHER]

This paper presents a variational-based approach for fusing hyperspectral and multispectral images. The fusion problem is formulated as an inverse problem whose solution is the target image assumed to live in a lower dimensional subspace. A sparse regularization term is carefully designed, relying on a decomposition of the scene on a set of dictionaries. The dictionary atoms and the supports of the corresponding active coding coefficients are learned from the observed images. Then, conditionally on these dictionaries and supports, the fusion problem is solved via alternating optimization with respect to the target image (using the alternating direction method of multipliers) and the coding coefficients. Simulation results demonstrate the efficiency of the proposed algorithm when compared with state-of-the-art fusion methods. [ABSTRACT FROM PUBLISHER]

Linear spectral unmixing is a challenging problem in hyperspectral imaging that consists of decomposing an observed pixel into a linear combination of pure spectra (or endmembers) with their corresponding proportions (or abundances). Endmember extraction algorithms can be employed for recovering the spectral signatures while abundances are estimated using an inversion step. Recent works have shown that exploiting spatial dependencies between image pixels can improve spectral unmixing. Markov random fields (MRF) are classically used to model these spatial correlations and partition the image into multiple classes with homogeneous abundances. This paper proposes to define the MRF sites using similarity regions. These regions are built using a self-complementary area filter that stems from the morphological theory. This kind of filter divides the original image into flat zones where the underlying pixels have the same spectral values. Once the MRF has been clearly established, a hierarchical Bayesian algorithm is proposed to estimate the abundances, the class labels, the noise variance, and the corresponding hyperparameters. A hybrid Gibbs sampler is constructed to generate samples according to the corresponding posterior distribution of the unknown parameters and hyperparameters. Simulations conducted on synthetic and real AVIRIS data demonstrate the good performance of the algorithm. [ABSTRACT FROM PUBLISHER]

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial postnonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated by simulations conducted on synthetic and real data. [ABSTRACT FROM AUTHOR]

Nonlinear models have recently shown interesting properties for spectral unmixing. This paper studies a generalized bilinear model and a hierarchical Bayesian algorithm for unmixing hyperspectral images. The proposed model is a generalization not only of the accepted linear mixing model but also of a bilinear model that has been recently introduced in the literature. Appropriate priors are chosen for its parameters to satisfy the positivity and sum-to-one constraints for the abundances. The joint posterior distribution of the unknown parameter vector is then derived. Unfortunately, this posterior is too complex to obtain analytical expressions of the standard Bayesian estimators. As a consequence, a Metropolis-within-Gibbs algorithm is proposed, which allows samples distributed according to this posterior to be generated and to estimate the unknown model parameters. The performance of the resulting unmixing strategy is evaluated via simulations conducted on synthetic and real data. [ABSTRACT FROM AUTHOR]

Accounting for endmember variability is a challenging issue when unmixing hyperspectral data. This paper models the variability that is associated with each endmember as a conical hull defined by extremal pixels from the data set. These extremal pixels are considered as so-called prototypal endmember spectra that have meaningful physical interpretation. Capitalizing on this data-driven modeling, the pixels of the hyperspectral image are then described as combinations of these prototypal endmember spectra weighted by bundling coefficients and spatial abundances. The proposed unmixing model not only extracts and clusters the prototypal endmember spectra, but also estimates the abundances of each endmember. The performance of the approach is illustrated thanks to experiments conducted on simulated and real hyperspectral data and it outperforms state-of-the-art methods. [ABSTRACT FROM AUTHOR]

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]

• This paper proposes a cofactorization method to perform jointly classification and representation learning. • The novel coupling approach produces a coherent and fully-interpretable hierarchical model. • The proposed model offers a rich interpretation of the data. • Performance is assessed on synthetic and real data in the specific context of hyperspectral image interpretation. Supervised classification and representation learning are two widely used classes of methods to analyze multivariate images. Although complementary, these methods have been scarcely considered jointly in a hierarchical modeling. In this paper, a method coupling these two approaches is designed using a matrix cofactorization formulation. Each task is modeled as a factorization matrix problem and a term relating both coding matrices is then introduced to drive an appropriate coupling. The link can be interpreted as a clustering operation over the low-dimensional representation vectors. The attribution vectors of the clustering are then used as features vectors for the classification task, i.e., the coding vectors of the corresponding factorization problem. A proximal gradient descent algorithm, ensuring convergence to a critical point of the objective function, is then derived to solve the resulting non-convex non-smooth optimization problem. An evaluation of the proposed method is finally conducted both on synthetic and real data in the specific context of hyperspectral image interpretation, unifying two standard analysis techniques, namely unmixing and classification. [ABSTRACT FROM AUTHOR]

Highlights • This paper proposes a unified framework to perform classification and low-level modeling jointly. • Robustness is improved by considering a possibly badly labeled training set. • The proposed model allows a very rich interpretation of the modeled data structure. • Performance is assessed on synthetic and real data in the specific context of hyperspectral image interpretation. • The proposed model is generic enough to incorporate any kind of low-level modeling. Abstract Within a supervised classification framework, labeled data are used to learn classifier parameters. Prior to that, it is generally required to perform dimensionality reduction via feature extraction. These preprocessing steps have motivated numerous research works aiming at recovering latent variables in an unsupervised context. This paper proposes a unified framework to perform classification and low-level modeling jointly. The main objective is to use the estimated latent variables as features for classification and to incorporate simultaneously supervised information to help latent variable extraction. The proposed hierarchical Bayesian model is divided into three stages: a first low-level modeling stage to estimate latent variables, a second stage clustering these features into statistically homogeneous groups and a last classification stage exploiting the (possibly badly) labeled data. Performance of the model is assessed in the specific context of hyperspectral image interpretation, unifying two standard analysis techniques, namely unmixing and classification. [ABSTRACT FROM AUTHOR]

When no arterial input function is available, quantification of dynamic PET images requires a previous step devoted to the extraction of a reference time-activity curve (TAC). Factor analysis is often applied for this purpose. This paper introduces a novel approach that conducts a new kind of nonlinear factor analysis relying on a compartment model, and computes the kinetic parameters of specific binding tissues jointly. To this end, it capitalizes on data-driven parametric imaging methods to provide a physical description of the underlying PET data, directly relating the specific binding with the kinetics of the non-specific binding in the corresponding tissues. This characterization is introduced into the factor analysis formulation to yield a novel nonlinear unmixing model designed for PET image analysis. This model also explicitly introduces global kinetic parameters that allow for a direct estimation of a binding potential that represents the ratio at equilibrium of specifically bound radioligand to the concentration of nondisplaceable radioligand in each non-specific binding tissue. The performance of the method is evaluated on synthetic and real data to demonstrate its potential interest. [Display omitted] • A new paradigm for dynamic PET factor analysis, relating the kinetics of specific and non-specific binding tissues. • Nonlinear unmixing is combined with a reference tissue compartment model. • Each non-specific binding tissue TAC is treated as a reference TAC. • Global kinetic parameters and reference tissue TACs are jointly estimated. • Recovered TACs are more accurately estimated by accounting for partial volume effect. [ABSTRACT FROM AUTHOR]

This paper presents a multiband image fusion algorithm based on unsupervised spectral unmixing for combining a high-spatial–low-spectral-resolution image and a low-spatial–high-spectral-resolution image. The widely used linear observation model (with additive Gaussian noise) is combined with the linear spectral mixture model to form the likelihoods of the observations. The nonnegativity and sum-to-one constraints resulting from the intrinsic physical properties of the abundances are introduced as prior information to regularize this ill-posed problem. The joint fusion and unmixing problem is then formulated as maximizing the joint posterior distribution with respect to the endmember signatures and abundance maps. This optimization problem is attacked with an alternating optimization strategy. The two resulting subproblems are convex and are solved efficiently using the alternating direction method of multipliers. Experiments are conducted for both synthetic and semi-real data. Simulation results show that the proposed unmixing-based fusion scheme improves both the abundance and endmember estimation compared with the state-of-the-art joint fusion and unmixing algorithms. [ABSTRACT FROM PUBLISHER]

This paper introduces a new dictionary learning strategy based on 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. We propose a practical formulation of this problem and introduce a Gauss-Seidel type algorithm referred to as alternative least square algorithm for its resolution. The search space of the proposed algorithm is of dimension $$KS$$ , which is typically smaller than the size of the target atom and much smaller than the size of the image. Moreover, the complexity of this algorithm is linear with respect to the image size, allowing larger atoms to be learned (as opposed to small patches). The conducted experiments show that we are able to accurately approximate atoms such as wavelets, curvelets, sinc functions or cosines for large values of K. The proposed experiments also indicate that the algorithm generally converges to a global minimum for large values of $$K$$ and $$S$$ . [ABSTRACT FROM AUTHOR]

For blind deconvolution of an unknown sparse sequence convolved with an unknown pulse, a powerful Bayesian method employs the Gibbs sampler in combination with a Bernoulli–Gaussian prior modeling sparsity. In this paper, we extend this method by introducing a minimum distance constraint for the pulses in the sequence. This is physically relevant in applications including layer detection, medical imaging, seismology, and multipath parameter estimation. We propose a Bayesian method for blind deconvolution that is based on a modified Bernoulli–Gaussian prior including a minimum distance constraint factor. The core of our method is a partially collapsed Gibbs sampler (PCGS) that tolerates and even exploits the strong local dependencies introduced by the minimum distance constraint. Simulation results demonstrate significant performance gains compared to a recently proposed PCGS. The main advantages of the minimum distance constraint are a substantial reduction of computational complexity and of the number of spurious components in the deconvolution result. [ABSTRACT FROM AUTHOR]

Exposure to influenza viruses is necessary, but not sufficient, for healthy human hosts to develop symptomatic illness. The host response is an important determinant of disease progression. In order to delineate host molecular responses that differentiate symptomatic and asymptomatic Influenza A infection, we inoculated 17 healthy adults with live influenza (H3N2/Wisconsin) and examined changes in host peripheral blood gene expression at 16 timepoints over 132 hours. Here we present distinct transcriptional dynamics of host responses unique to asymptomatic and symptomatic infections. We show that symptomatic hosts invoke, simultaneously, multiple pattern recognition receptors-mediated antiviral and inflammatory responses that may relate to virus-induced oxidative stress. In contrast, asymptomatic subjects tightly regulate these responses and exhibit elevated expression of genes that function in antioxidant responses and cell-mediated responses. We reveal an ab initio molecular signature that strongly correlates to symptomatic clinical disease and biomarkers whose expression patterns best discriminate early from late phases of infection. Our results establish a temporal pattern of host molecular responses that differentiates symptomatic from asymptomatic infections and reveals an asymptomatic host-unique non-passive response signature, suggesting novel putative molecular targets for both prognostic assessment and ameliorative therapeutic intervention in seasonal and pandemic influenza. [ABSTRACT FROM AUTHOR]

Bayesian positive source separation (BPSS) is a useful unsupervised approach for hyperspectral data unmixing, where numerical nonnegativity of spectra and abundances has to be ensured, such as in remote sensing. Moreover, it is sensible to impose a sum-to-one (full additivity) constraint to the estimated source abundances in each pixel. Even though nonnegativity and full additivity are two necessary properties to get physically interpretable results, the use of BPSS algorithms has so far been limited by high computation time and large memory requirements due to the Markov chain Monte Carlo calculations. An implementation strategy that allows one to apply these algorithms on a full hyperspectral image, as it is typical in earth and planetary science, is introduced. The effects of pixel selection and the impact of such sampling on the relevance of the estimated component spectra and abundance maps, as well as on the computation times, are discussed. For that purpose, two different data sets have been used: a synthetic one and a real hyperspectral image from Mars. [ABSTRACT FROM AUTHOR]