A simplified exposition of sparsity inducing penalty functions for denoising

Abstract

This paper attempts to provide a pedagogical view to the approach of denoising using non-convex regularization developed by Ankit Parekh et al. The present paper proposes a simplified signal denoising approach by explicitly using sub-band matrices of decimated wavelet transform matrix. The objective function involves convex and non-convex terms in which the convexity of the overall function is restrained by parameterized non-convex term. The solution to this convexoptimization problem is obtained by employing Majorization-Minimization iterative algorithm. For the experimentation purpose, different wavelet filters such as daubechies, coiflets and reverse biorthogonal were used.