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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]

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]

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]

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 modeling 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. • Multimodal change detection is formulated as a coupled dictionary learning problem. • The method is able to handle multimodal images with possibly different resolution. • Coupled dictionary learning and codes estimated using alternating optimization. • Algorithmic solution for nonconvex problem with convergence to critical point. • The performance is assessed on a comprehensive set of experiments. [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]

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]

• A partial acquisition was implemented on a scanning transmission electron microscope. • This speeds up electron energy loss spectroscopy and preserves sensitive materials. • A potentially online reconstruction algorithm is required to get exploitable images. • We propose a fast and efficient algorithm that fulfills these requirements. • The results are comparable to state-of-the-art, with a drastically lower run-time. This paper discusses the reconstruction of partially sampled spectrum-images to accelerate the acquisition in scanning transmission electron microscopy (STEM). The problem of image reconstruction has been widely considered in the literature for many imaging modalities, but only a few attempts handled 3D data such as spectral images acquired by STEM electron energy loss spectroscopy (EELS). Besides, among the methods proposed in the microscopy literature, some are fast but inaccurate while others provide accurate reconstruction but at the price of a high computation burden. Thus none of the proposed reconstruction methods fulfills our expectations in terms of accuracy and computation complexity. In this paper, we propose a fast and accurate reconstruction method suited for atomic-scale EELS. This method is compared to popular solutions such as beta process factor analysis (BPFA) which is used for the first time on STEM-EELS images. Experiments based on real as synthetic data will be conducted. [ABSTRACT FROM AUTHOR]

In the context of spectral unmixing, essential information corresponds to the most linearly dissimilar rows and/or columns of a two-way data matrix which are indispensable to reproduce the full data matrix in a convex linear way. Essential information has recently been shown accessible on-the-fly via a decomposition of the measured spectra in the Fourier domain and has opened new perspectives for fast Raman hyperspectral microimaging. In addition, when some spatial prior is available about the sample, such as the existence of homogeneous objects in the image, further acceleration for the data acquisition procedure can be achieved by using superpixels. The expected gain in acquisition time is shown to be around three order of magnitude on simulated and real data with very limited distortions of the estimated spectrum of each object composing the images.

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 half quadratic splitting method (HQS) and 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 and PnP-HQS) 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.

In the context of multivariate curve resolution (MCR) and spectral unmixing, essential information (EI) corresponds to the most linearly dissimilar rows and/or columns of a two-way data matrix. In recent works, the assessment of EI has been revealed to be a very useful practical tool to select the most relevant spectral information before MCR analysis, key features being speed and compression ability. However, the canonical approach relies on the principal component analysis to evaluate the convex hull that encapsulates the data structure in the normalized score space. This implies that the evaluation of the essentiality of each spectrum can only be achieved after all the spectra have been acquired by the instrument. This paper proposes a new approach to extract EI in the Fourier domain (EIFD). Spectral information is transformed into Fourier coefficients, and EI is assessed from a convex hull analysis of the data point cloud in the 2D phasor plots of a few selected harmonics. Because the coordinate system of a phasor plot does not depend on the data themselves, the evaluation of the essentiality of the information carried by each spectrum can be achieved individually and independently from the others. As a result, time-consuming operations like Raman spectral imaging can be significantly accelerated exploiting a chemometric-driven (i.e., based on the EI content of a spectral pixel) procedure for data acquisition and targeted sampling. The usefulness of EIFD is shown by analyzing Raman hyperspectral microimaging data, demonstrating a potential 50-fold acceleration of Raman acquisition.

When adopting a model-based formulation, solving inverse problems encountered in multiband imaging requires to define spatial and spectral regularizations. In most of the works of the literature, spectral information is extracted from the observations directly to derive data-driven spectral priors. Conversely, the choice of the spatial regularization often boils down to the use of conventional penalizations (e.g., total variation) promoting expected features of the reconstructed image (e.g., piece-wise constant). In this work, we propose a generic framework able to capitalize on an auxiliary acquisition of high spatial resolution to derive tailored data-driven spatial regularizations. This approach leverages on the ability of deep learning to extract high level features. More precisely, the regularization is conceived as a deep generative network able to encode spatial semantic features contained in this auxiliary image of high spatial resolution. To illustrate the versatility of this approach, it is instantiated to conduct two particular tasks, namely multiband image fusion and multiband image inpainting. Experimental results obtained on these two tasks demonstrate the benefit of this class of informed regularizations when compared to more conventional ones.

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 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.

This paper proposes a fast multi-band image fusion algorithm, which combines a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The well admitted forward model is explored to form the likelihoods of the observations. Maximizing the likelihoods leads to solving a Sylvester equation. By exploiting the properties of the circulant and downsampling matrices associated with the fusion problem, a closed-form solution for the corresponding Sylvester equation is obtained explicitly, getting rid of any iterative update step. Coupled with the alternating direction method of multipliers and the block coordinate descent method, the proposed algorithm can be easily generalized to incorporate prior information for the fusion problem, allowing a Bayesian estimator. Simulation results show that the proposed algorithm achieves the same performance as the existing algorithms with the advantage of significantly decreasing the computational complexity of these algorithms.

This paper addresses the problem of estimating the Potts parameter β jointly with the unknown parameters of a Bayesian model within a Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because performing inference on β requires computing the intractable normalizing constant of the Potts model. In the proposed MCMC method, the estimation of β is conducted using a likelihood-free Metropolis-Hastings algorithm. Experimental results obtained for synthetic data show that estimating β jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of β. On the other hand, choosing an incorrect value of β can degrade estimation performance significantly. To illustrate the interest of this method, the proposed algorithm is successfully applied to real bidimensional SAR and tridimensional ultrasound images.