Robust Compressed Sensing based on Correntropy and Smoothly Clipped Absolute Deviation Penalty

Robust compressed sensing aiming to reconstruct a signal from its noisy and compressed measurements has attracted considerable interest in recent years. Traditional compressed sensing methods are usually developed based on the ℓ
₂
- norm data fidelity and only perform well under Gaussian noise. In this study, a new formulation based on the correntropy, which has the capability of suppressing the large outliers, is presented for robust compressed sensing under non-Gaussian noise. Meanwhile, in this formulation, the smoothly clipped absolute deviation (SCAD) regularization is exploited for sparsity inducing. By combining half-quadratic technique and alternating direction method of multipliers (ADMM), a new effective algorithm, named as HQADM, is derived to optimize the new formulation. Comparative experiments with several typical robust compressed sensing algorithms are given to show the effectiveness of the proposed algorithm.