This paper considers the denoising problem from the viewpoint of sparse atomic representation. A general framework of time-frequency soft-thresholding is proposed which encompasses and connects well-known shrinkage operators as special cases. In particular, the groundbreaking idea of exploiting signal sparsity in the framework of redundant representations is extended to incorporate knowledge about structural properties of the observed signals. Convergence of the corresponding algorithms is numerically evaluated and their performance in denoising real-life audio signals is compared to the results of similar existing approaches. The novel approach is competitive with respect to signal to noise ratio and improves the state of the art in terms of perceptual criteria.
https://www.aes.org/e-lib/browse.cfm?elib=16182
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