Hierarchical Bayesian image analysis: from low-level modeling to robust supervised learning

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

Hyperspectral image unmixing with LiDAR data-aided spatial regularization

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

Modèle bayésien hiérarchique pour le démélange et la classification robuste d'images hyperspectrales

L’interprétation des images hyperspectrales demeure un problème complexe qui a été abordée sous différents paradigmes. En particulier, les techniques de classification supervisée et de démélange spectral sont deux familles de méthodes d’interprétation largement utilisées. Ces deux approches offrent des analyses complémentaires : le démélange spectral propose une modélisation basée sur une interprétation physique des images hyperspectrales, en supposant que chaque pixel est un mélange de spectres purs associés aux divers matériaux présents dans la scène, tandis que la classification supervisée cherche à identifier une classe unique par pixel en se basant sur un ensemble de classes sémantiques définies par l’utilisateur et sur un ensemble de données, labellisées par un expert, lui servant d’exemple. Si ces deux techniques ont été largement discutées dans la littérature, elles ont été rarement utilisées conjointement

Factorisation de matrices pour le démélange et la classification conjoints d'images hyperspectrales

La classification supervisée et le démélange spectral sont parmi les techniques les plus utilisées pour extraire l’information d’images hyperspectrales. Bien que ces deux méthodes sont couramment utilisées, elles n’ont que très rarement été envisagées conjointement. Au lieu d’utiliser ces méthodes de manière séquentielle, comme on le voit les travaux déjà réalisés [1], nous proposons ici d’introduire le concept de démélange et classification conjoints

Hyperspectral unmixing with spectral variability using adaptive bundles and double sparsity

International audienceSpectral variability is one of the major issue when conducting hyperspectral unmixing. Within a given image composed of some elementary materials (herein referred to as endmember classes), the spectral signature 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

Hierarchical Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing with Spectral Variability

International audienceAccounting 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

A multiple endmember mixing model to handle spectral variability

International audienceThis paper proposes a novel mixing model that incorporates spectral variability. The proposed approach relies on the following two ingredients: i) a mixed spectrum is modeled as a combination of a few endmember signatures which belong to some endmember bundles (referred to as classes), ii) sparsity is promoted for the selection of both endmember classes and endmember spectra within a given class. This leads to an adaptive and hierarchical description of the endmember spectra. A proximal alternating linearized minimization algorithm is derived to minimize the objective function associated with this model, providing estimates of the bundling coefficients and abundances. Results showed that the proposed method outperformed the existing methods in terms of promoting sparsity and selecting endmember classes within each pixel

LiDAR-driven spatial regularization for hyperspectral unmixing

International audienceOnly a few research works consider LiDAR data while conducting hyperspectral image unmixing. However, the digital surface model derived from LiDAR can provide meaningful information, in particular when spatially regularizing the inverse problem underlain by spectral unmixing. This paper proposes a general framework for spectral unmixing that incorporates LiDAR data to inform the spatial regularization applied to the abundance maps. The proposed framework is validated and compared to existing unmixing methods that incorporate spatial information derived from the hyperspectral image itself using two different simulated data and digital surface models. Results show that the spatial regularization incorporating LiDAR data significantly improves abundance estimates

A multiple endmember mixing model to handle spectral variability in hyperspectral unmixing

This paper proposes a novel mixing model that incorporates spectral variability. The proposed approach relies on the following two ingredients: i) a mixed spectrum is modeled as a combination of a few endmember signatures which belong to some endmember bundles (referred to as classes), ii) sparsity is promoted for the selection of both endmember classes and endmember spectra within a given class. This leads to an adaptive and hierarchical description of the endmember spectra. A proximal alternating linearized minimization algorithm is derived to minimize the objective function associated with this model, providing estimates of the bundling coefficients and abundances. Results showed that the proposed method outperformed the existing methods in terms of promoting sparsity and selecting endmember classes within each pixel

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

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