A Fast Iterative Method for Removing Sparse Noise from Sparse Signals
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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 problem investigated in this paper arises in different applications such as impulsive noise cancellation from images and audios, and decomposition of low-rank and sparse components of matrices. First, we provide a cost function for our problem and then present an iterative method to find its local minimum. The convergence analysis of the algorithm is also provided. As an application of this problem, we apply our algorithm for impulsive noise (salt-andpepper noise and random-valued impulsive noise) 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 is simple and fast, and it outperforms the other state-of-the-art methods in terms of reconstruction quality and/or complexity.
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