A $ q$ -Gaussian Maximum Correntropy Adaptive Filtering Algorithm for Robust Spare Recovery in Impulsive Noise

This letter proposes a robust formulation for sparse signal reconstruction from compressed measurements corrupted by impulsive noise, which exploits the $\boldsymbol {q}$ -Gaussian generalized correntropy $\boldsymbol {(1 as the loss function for the residual error and utilizes a $\ell _{0}$ -norm penalty term for sparsity inducing. To solve this formulation efficiently, we develop a gradient-based adaptive filtering algorithm which incorporates a zero-attracting regularization term into the framework of adaptive filtering. This new proposed algorithm blending the advantages of adaptive filtering and $\boldsymbol {q}$ -Gaussian generalized correntropy can obtain accurate reconstruction and satisfactory robustness with a proper shape parameter $\boldsymbol {q}$ . Numerical experiments on both synthetic sparse signals and natural images are conducted to illustrate the superior recovery performance of the proposed algorithm to the state-of-the-art robust sparse signal reconstruction algorithms.