A Fast Iterative Method for Removing Impulsive Noise From Sparse Signals

In this paper, we propose a new method to reconstruct a signal corrupted by noise where both signal and noise are sparse but in different domains. The main contribution of our algorithm is its low complexity; it has much lower run-time than most other algorithms. The reconstruction quality of our algorithm is both objectively (in terms of PSNR and SSIM) and subjectively better or comparable to other state-of-the-art algorithms. We provide a cost function for our problem, present an iterative method to find its local minimum, and provide the analysis of the algorithm. As an application of this problem, we apply our algorithm for Salt-and-Pepper noise (SPN) and Random-Valued Impulsive Noise (RVIN) removal from images and compare our results with other notable algorithms in the literature. Furthermore, we apply our algorithm for removing clicks from audio signals. Simulation results show that our algorithms are simple and fast, and it outperforms other state-of-the-art methods in terms of reconstruction quality and/or complexity.