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.
Highlights
Spectral unmixing (SU) of hyperspectral images has attracted growing interest over the last few decades
This algorithm is based on a nonlinear mixing model inspired from residual component analysis (RCA) [22]
1) this model reduces to the classical linear mixing model (LMM) for φn = 0L, 2) the model (1) is general enough to handle different of kinds of nonlinearities such as the bilinear model studied in [12] (referred to as Fan model (FM)), the generalized bilinear model (GBM) [13], and the polynomial post-nonlinear mixing model (PPNMM) studied for nonlinear spectral unmixing in [18] and nonlinearity detection in [20]
Summary
Spectral unmixing (SU) of hyperspectral images has attracted growing interest over the last few decades. Nonlinear mixing models (NLMMs) provide an interesting alternative to overcoming the inherent limitations of the LMM They have been proposed in the hyperspectral image literature and can be divided into two main classes [8]. This paper presents a new supervised Bayesian algorithm for joint nonlinear SU and nonlinearity detection This algorithm is supervised in the sense that the endmembers contained in the image are assumed to be known (chosen from a spectral library or extracted from the data by an endmember extraction algorithm (EEA)). This algorithm is based on a nonlinear mixing model inspired from residual component analysis (RCA) [22].
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