A Regular k-Shrinkage Thresholding Operator for the Removal of Mixed Gaussian-Impulse Noise

Abstract

The removal of mixed Gaussian-impulse noise plays an important role in many areas, such as remote sensing. However, traditional methods may be unaware of promoting the degree of the sparsity adaptively after decomposing into low rank component and sparse component. In this paper, a new problem formulation with regular spectral k-support norm and regular k-support l1 norm is proposed. A unified framework is developed to capture the intrinsic sparsity structure of all two components. To address the resulting problem, an efficient minimization scheme within the framework of accelerated proximal gradient is proposed. This scheme is achieved by alternating regular k-shrinkage thresholding operator. Experimental comparison with the other state-of-the-art methods demonstrates the efficacy of the proposed method.