Sparse regularization method for the detection and removal of random-valued impulse noise

In this paper, we propose a novel two-stage algorithm for the detection and removal of random-valued impulse noise using sparse representations. The main aim of the paper is to demonstrate the strength of image inpainting technique for the reconstruction of images corrupted by random-valued impulse noise at high noise densities. First, impulse locations are detected by applying the combination of sparse denoising and thresholding, based on sparse and overcomplete representations of the corrupted image. This stage optimally selects threshold values so that the sum of the number of false alarms and missed detections obtained at a particular noise level is the minimum. In the second stage, impulses, detected in the first stage, are considered as the missing pixels or holes and subsequently these holes are filled-up using an image inpainting method. Extensive simulation results on standard gray scale images show that the proposed method successfully removes randomvalued impulse noise with better preservation of edges and other details compared to the existing techniques at high noise ratios.