Compressive hyper-spectral imaging in the presence of impulse noise

There have been a number of studies for addressing the recovery of compressively sampled hyper-spectral images in the presence of Gaussian noise; this work proposes a recovery technique in the presence of impulse noise. Owing to the sparse nature of the impulse noise, the data fidelity term is an L1-norm. The hyper-spectral datacube is modeled as a combination of sparse transform coefficients and a low-rank matrix. The resulting optimization problem is solved using the split-Bregman approach. The success of the proposed method is shown using the numerical results and visual evaluation.