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Deep Unfolded Iterative Shrinkage-Thresholding Model for Hyperspectral Unmixing

In this paper, we propose a novel approach for spectral unmixing by unfolding the iterative shrinkage-thresholding algorithm (ISTA) into a deep neural network architecture. Spectral unmixing aims at identifying the endmembers and their fractional abundances in the mixed pixels. Once the endmembers are obtained as a dictionary, abundance estimation can be defined as a sparse coding problem with nonnegativity constraint. There are a number of iterative optimization algorithms for solving this problem, including ISTA, however, they always require hundreds and even thousands iterations, which is too slow for time-sensitive applications. In contrast, deep neural networks can approximate a finite closed-form expression to direct estimate abundances by learning from training samples, but they are closer to black-box mechanism rather than problem-level formulations. Deep unfolding constructs a deep neural network architecture inspired by the problem model and its corresponding optimization algorithm, which incorporates the prior knowledge of physical model and algorithm into network architecture. In this paper, the deep unfolded ISTA model is adopted for abundance estimation. It uses only a small training set to learn the model parameters, and then the abundance estimation become to be a feed-forward process in this model, which is very fast since no iteration is required.