A new non-convex sparse optimization method for image restoration

Abstract

In the field of image processing, total variational model is an effective prior model. In order to better eliminate impulse noise, an effective method is to use $\ell _{1}{\textit{-norm}}$ total variational model. However, the TV image recovery always produces staircase artifacts, and the $\ell _{1}{\textit{-norm}}$ excessively penalizes the signal entries. Therefore, in this paper, a new total variational model is proposed to eliminate the staircase effects and impulse noise. We use $\ell _{0}{\textit{-norm}}$ as the data fidelity term to eliminate impulse noise and the hybrid total variation as the regularization term to effectively eliminate staircase artifacts. In order to effectively tackle the proposed $\ell _{0}{\textit{-norm}}$ and hybrid total variation, we first express this problem as a Mathematical Program with Equilibrium Constraints(MPEC), and then a Proximal Alternating Direction Method of Multipliers(PADMM) is adopted to solve this problem. In the experimental part, we adopt three indices: ${\textit{SNR}}_{0}$, ${\textit{SNR}}_{1}$ and ${\textit{SNR}}_{2}$ to measure the quality of image restoration. When the value of the ${\textit{SNR}}$ tends to be stable, then each algorithm stops iteration. Numerical simulation results show that the proposed method has better performance in removing impulse noise, suppressing staircase effect and preserving image edge information.