Reconstruction of wavelet coefficients using total variation minimization

Abstract : 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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Sylvain Durand, Jacques Froment. Reconstruction of wavelet coefficients using total variation minimization. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2003, 24 (5), pp.1754-1767. ⟨hal-00204982⟩

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