Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 24, Issue 5, Pages 1754-1767Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S1064827501397792
Keywords
wavelet; total variation; denoising; subgradient method
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We propose a model to reconstruct wavelet coefficients using a total variation minimization algorithm. The approach is motivated by wavelet signal denoising methods, where thresholding small wavelet coefficients leads to pseudo-Gibbs artifacts. By replacing these thresholded coefficients by values minimizing the total variation, our method performs a nearly artifact-free signal denoising. In this paper, we detail the algorithm based on a subgradient descent combining a projection on a linear space. The convergence of the algorithm is established and numerical experiments are reported.
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