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In this paper, we propose a new method to reconstruct a signal corrupted bynoise where both signal and noise are sparse but in different domains. Theproblem investigated in this paper arises in different applications such asimpulsive noise removal from images, audios and videos, decomposition oflow-rank and sparse components of matrices, and separation of texts fromimages. First, we provide a cost function for our problem and then present aniterative method to find its local minimum. The analysis of the algorithm isalso provided. As an application of this problem, we apply our algorithm forimpulsive noise Salt-and-Pepper noise (SPN) and Random-Valued Impulsive Noise(RVIN)) removal from images and compare our results with other notablealgorithms in the literature. Furthermore, we apply our algorithm for removingclicks from audio signals. Simulation results show that our algorithms issimple and fast, and it outperforms other state-of-the-art methods in terms ofreconstruction quality and/or complexity.

A Fast Iterative Method for Removing Impulsive Noise from Sparse Signals