A Probabilistic Joint Sparse Regression Model for Semisupervised Hyperspectral Unmixing

Semisupervised hyperspectral unmixing finds the ratio of spectral library members in the mixture of hyperspectral pixels to find the proportion of pure materials in a natural scene. The two main challenges are noise in observed spectral vectors and high mutual coherence of spectral libraries. To tackle these challenges, we propose a probabilistic sparse regression method for linear hyperspectral unmixing, which utilizes the implicit relations of neighboring pixels. We partition the hyperspectral image into rectangular patches. The sparse coefficients of pixels in each patch are assumed to be generated from a Laplacian scale mixture model with the same latent variables. These latent variables specify the probability of existence of endmembers in the mixture of each pixel. Experiments on synthetic and real hyperspectral images illustrate the superior performance of the proposed method over alternatives.