Simultaneous Nonconvex Denoising and Unmixing for Hyperspectral Imaging

Sparse hyperspectral unmixing aims at finding the sparse fractional abundance vector of a spectral signature present in a mixed pixel. However, there are several types of noise present in the hyperspectral images. These are called mixed noise including stripes, impulse noise and Gaussian noise which deteriorate the performance of sparse unmixing algorithms. In this study, we simultaneously unmix and denoise the hyperspectral image in a unified framework in the presence of mixed noise. In the denoising step, we utilize a low-rank and sparse decomposition based on a nonconvex approach to approximate the rank of hyperspectral data and eliminate the sparse noise terms. In the unmixing part, we employ a semi-supervised sparse unmixing algorithm which uses a nonconvex heuristic similar to denoising step to promote the sparsity of the abundance matrix. We conduct several experiments on synthetic and real hyperspectral data sets to validate the effectiveness of the proposed method in denoising and unmixing processes.