Hyper-spectral impulse denoising: A row-sparse Blind Compressed Sensing formulation

This paper addresses the problem of impulse denoising from hyper-spectral images. Impulse noise is sparse; removing impulse noise requires minimizing an l₁-norm data fidelity term. Prior studies have exploited the intra-band spatial correlation (leading to sparsity in transform domain) and inter-band spectral-correlation (joint-sparsity) of hyper-spectral images for Gaussian denoising. In this work, we propose to learn the joint-sparsity promoting dictionary adaptively from the data for impulse denoising problems. Unlike dictionary learning techniques, the sparsifying dictionary is not learnt in an offline training phase. We follow the Blind Compressed Sensing (BCS) framework - dictionary learning and denoising proceeds simultaneously. The optimization problem that arises out of our formulation is solved using the Split Bregman approach. The proposed algorithm, when compared against prior techniques (on real hyper-spectral datasets) shows more than 5dB improvement in PSNR on average.