Nonlinear Filtered Compressed Sensing Applied on Image De-noising

Abstract

In the present era, the need for studies on noise removal by image processing is still considerable. In this paper, we developed a compressed sensing (CS) based algorithm for image de-nosing. Optimization theory was utilized. A cost function consisting of data fidelity term and penalty term was proposed. The minimization of cost function was achieved by proximal minimization method. The advantage of the algorithm is two-fold. First, we embedded the filtering procedure into a CS framework. It enhanced the effectiveness of filtering strategy. As known, repetitive post filters make images blurred, but CS in the proposed algorithm could keep the image clarity while achieving noise depression. Second, selectivity of filter type, especially nonlinear filters, strengthened the effectiveness and practicability of CS. With increasing number of literatures revealing the failure of total variation (TV) method in processing images with rich details, the new algorithm could preserve image textures and object boundaries accurately. Convergence property of the novel algorithm was also proved by the de-nosing instance. Among the nonlinear filters, nonlocal weighted median filter based CS presented the best de-noising effectiveness. The algorithm is considered to have a potential application value in other image processing issues, such as image restoration and reconstruction.