research-article

Reconstruction of Wavelet Coefficients Using Total Variation Minimization

Authors:

Sylvain Durand,

Jacques FromentAuthors Info & Claims

SIAM Journal on Scientific Computing, Volume 24, Issue 5

Pages 1754 - 1767

https://doi.org/10.1137/S1064827501397792

Published: 01 January 2003 Publication History

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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cover image SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing Volume 24, Issue 5

2003

373 pages

ISSN:1064-8275

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Copyright © 2003 Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2003

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Cited By

Charmouti BJunoh AAbdurrazzaq AMashor M(2022)A new denoising method for removing salt & pepper noise from imageMultimedia Tools and Applications10.1007/s11042-021-11615-381:3(3981-3993)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1007/s11042-021-11615-3
Song YWu PGilmore DLi Q(2021)A Spatial Heterogeneity-Based Segmentation Model for Analyzing Road Deterioration Network Data in Multi-Scale Infrastructure SystemsIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2020.300119322:11(7073-7083)Online publication date: 1-Nov-2021
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Prateek GJu YNehorai A(2021)Sparsity-Assisted Signal Denoising and Pattern Recognition in Time-Series DataCircuits, Systems, and Signal Processing10.1007/s00034-021-01774-x41:1(249-298)Online publication date: 3-Jul-2021
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Shahdoosti HHazavei S(2019)A new compressive sensing based image denoising method using block-matching and sparse representations over learned dictionariesMultimedia Tools and Applications10.1007/s11042-018-6818-378:9(12561-12582)Online publication date: 1-May-2019
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Jiang LYin H(2018)Wavelet inpainting by fractional order total variationMultidimensional Systems and Signal Processing10.1007/s11045-016-0465-529:1(299-320)Online publication date: 1-Jan-2018
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Shahdoosti HHazavei S(2018)Combined ripplet and total variation image denoising methods using twin support vector machinesMultimedia Tools and Applications10.1007/s11042-017-4618-977:6(7013-7031)Online publication date: 1-Mar-2018
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Scarnati TGelb APlatte R(2018)Using $$\ell _1$$ℓ1 Regularization to Improve Numerical Partial Differential Equation SolversJournal of Scientific Computing10.1007/s10915-017-0530-875:1(225-252)Online publication date: 1-Apr-2018
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Preciozzi JGonzález MAlmansa AMusé P(2017)Joint denoising and decompression: A patch-based Bayesian approach2017 IEEE International Conference on Image Processing (ICIP)10.1109/ICIP.2017.8296482(1252-1256)Online publication date: 17-Sep-2017
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Shahdoosti HKhayat O(2016)Combination of anisotropic diffusion and non-subsampled shearlet transform for image denoisingJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/IFS-15203530:6(3087-3098)Online publication date: 1-Jan-2016
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