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Artifact-Free Wavelet Denoising: Non-convex Sparse Regularization, Convex Optimization

Author:
Ding, Yin   Selesnick, Ivan W.   


Journal:
IEEE Signal Processing Letters


Issue Date:
2015


Abstract(summary):

Algorithms for signal denoising that combine wavelet-domain sparsity and total variation (TV) regularization are relatively free of artifacts, such as pseudo-Gibbs oscillations, normally introduced by pure wavelet thresholding. This paper formulates wavelet-TV (WATV) denoising as a unified problem. To strongly induce wavelet sparsity, the proposed approach uses non-convex penalty functions. At the same time, in order to draw on the advantages of convex optimization (unique minimum, reliable algorithms, simplified regularization parameter selection), the non-convex penalties are chosen so as to ensure the convexity of the total objective function. A computationally efficient, fast converging algorithm is derived.


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