When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are multi-scattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this paper, we present an overview of recent advances in nonlinear unmixing modeling. MOTIVATION FOR NONLINEAR MODELS Spectral unmixing (SU) is widely used for analyzing hyperspectral data arising in areas such as: remote sensing, planetary science chemometrics, materials science and other areas of micro-spectroscopy. SU provides a comprehensive

Abstract — This paper presents a nonlinear mixing model for joint hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are linear combinations of known pure spectral components corrupted by an additional nonlinear term, affecting the end members and contaminated by an additive Gaussian noise. A Markov random field is considered for nonlinearity detection based on the spatial structure of the nonlinear terms. The observed image is segmented into regions where nonlinear terms, if present, share similar statistical properties. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint nonlinear unmixing and nonlinearity detection algorithm. The performance of the proposed strategy is first evaluated on synthetic data. Simulations conducted with real data show the accuracy of the proposed unmixing and nonlinearity detection strategy for the analysis of hyperspectral images. Index Terms — Hyperspectral imagery, nonlinear spectral unmixing, residual component analysis, nonlinearity detection.

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.

hen considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid, and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate inter-actions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this article, we present an overview of recent advances in nonlinear unmixing modeling. MOTIVATION FOR NONLINEAR MODELS Spectral unmixing (SU) is widely used for analyzing hyperspectral data arising in areas such as remote sensing, planetary science chemometrics, materials science, and other areas of microspec-troscopy. SU provides a comprehensive and quantitative mapping of the elementary materials that are present in the acquired data. More precisely, SU can identify the spectral signatures of these materials (usually called endmembers) and can estimate their relative contributions (known as abundances) to the measured spectra. Similar to other blind source separation tasks, the SU problem is naturally ill posed and admits a wide range of admissi-ble solutions. As a consequence, SU is a challenging problem that has received considerable attention in the remote sensing, signal, and image processing communities [1]. Hyperspectral data analy-sis can be supervised, when the endmembers are known, or unsupervised, when they are unknown. Irrespective of the case, W

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. ha l-0

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in:

Bayesian algorithm for unsupervised unmixing of hyperspectral images

This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundance vectors associated with the pure spectral components. We assume that the spectral signatures of the pure components and the nonlinear function are unknown. The first step of the proposed method estimates the abundance vectors for all the image pixels using a Gaussian process latent variable model. The endmembers are subsequently estimated using Gaussian process regression. The performance of the unmixing strategy is compared with state-of-the-art unmixing strategies on synthetic data. One of the interesting properties of the proposed strategy is its robustness to the absence of pure pixels in the image. Index Terms — Hyperspectral images, nonlinear spectral unmixing, unsupervised unmixing, Gaussian process regression, Bayesian estimation. 1.

This paper presents a nonlinear mixing model for joint hyperspectral image unmixing and nonlinearity detection. The proposed model as-sumes that the pixel reflectances are linear mixtures of endmembers, corrupted by an additional nonlinear term and an additive Gaussian noise. A Markov random field is considered for nonlinearity de-tection based on the spatial structure of the nonlinear terms. The observed image is segmented into regions where nonlinear terms, if present, share similar statistical properties. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint nonlinear unmixing and nonlinearity detection algorithm. Sim-ulations conducted with synthetic and real data show the accuracy of the proposed unmixing and nonlinearity detection strategy for the analysis of hyperspectral images. Index Terms — Hyperspectral imagery, nonlinear spectral un-mixing, residual component analysis, nonlinearity detection. 1.

Abstract — This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are post-nonlinear functions of unknown pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using second-order polynomials leading to a polynomial post-nonlinear mixing model. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding an unsupervised nonlinear unmixing algorithm. Due to the large number of parameters to be estimated, an efficient Hamiltonian Monte Carlo algorithm is investigated. The classical leapfrog steps of this algorithm are modified to handle the parameter constraints. The performance of the unmixing strategy, including convergence and parameter tuning, is first evaluated on synthetic data. Simulations conducted with real data finally show the accuracy of the proposed unmixing strategy for the analysis of hyperspectral images. Index Terms — Hyperspectral imagery, unsupervised spectral unmixing, Hamiltonian Monte Carlo, post-nonlinear model.