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Nonlinear Unmixing of Hyperspectral Images: Models and Algorithms
"... 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 mul ..."
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Cited by 13 (4 self)
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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.
Residual component analysis of hyperspectral images -- Application to joint nonlinear unmixing and nonlinearity detection
, 2014
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Unsupervised Post-Nonlinear Unmixing of Hyperspectral Images Using a Hamiltonian Monte Carlo Algorithm
, 2014
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BAYESIAN ALGORITHM FOR UNSUPERVISED UNMIXING OF HYPERSPECTRAL IMAGES USING A POST-NONLINEAR MODEL
"... 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. The nonlinear effects are approximated by a polynom ..."
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Cited by 1 (1 self)
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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. The nonlinear effects are approximated by a polynomial 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 constrained Hamiltonian Monte Carlo algorithm is investigated. The performance of the unmixing strategy is finally evaluated on synthetic data. Index Terms — Hyperspectral imagery, unsupervised spectral unmixing, Hamiltonian Monte Carlo, post-nonlinear model.
NONLINEAR HYPERSPECTRAL UNMIXING USING GAUSSIAN PROCESSES
, 2013
"... 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 p ..."
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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.
RESIDUAL COMPONENT ANALYSIS OF HYPERSPECTRAL IMAGES FOR JOINT NONLINEAR UNMIXING AND NONLINEARITY DETECTION
"... 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 i ..."
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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.
