Total variation wavelet thresholding

Tony F. Chan; Hao Min Zhou

doi:10.1007/s10915-007-9133-0

Total variation wavelet thresholding

Tony F. Chan, Hao Min Zhou^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

Abstract

We propose using Partial Differential Equation (PDE) techniques in wavelet based image processing to remove noise and reduce edge artifacts generated by wavelet thresholding. We employ a variational framework, in particular the minimization of total variation (TV), to select and modify the retained wavelet coefficients so that the reconstructed images have fewer oscillations near edges while noise is smoothed. Numerical experiments show that this approach improves the reconstructed image quality in wavelet compression and in denoising.

Original language	English (US)
Pages (from-to)	315-341
Number of pages	27
Journal	Journal of Scientific Computing
Volume	32
Issue number	2
DOIs	https://doi.org/10.1007/s10915-007-9133-0
State	Published - Aug 2007
Externally published	Yes

Bibliographical note

Funding Information:
Research supported in part by grants ONR-N00017-96-1-0277, NSF DMS-9973341 and DMS-0410062 and NIH contract P 20 MH65166.

Keywords

Image processing
Total variation minimization
Wavelet

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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10.1007/s10915-007-9133-0

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keywords = "Image processing, Total variation minimization, Wavelet",

author = "Chan, {Tony F.} and Zhou, {Hao Min}",

note = "Funding Information: Research supported in part by grants ONR-N00017-96-1-0277, NSF DMS-9973341 and DMS-0410062 and NIH contract P 20 MH65166.",

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N2 - We propose using Partial Differential Equation (PDE) techniques in wavelet based image processing to remove noise and reduce edge artifacts generated by wavelet thresholding. We employ a variational framework, in particular the minimization of total variation (TV), to select and modify the retained wavelet coefficients so that the reconstructed images have fewer oscillations near edges while noise is smoothed. Numerical experiments show that this approach improves the reconstructed image quality in wavelet compression and in denoising.

AB - We propose using Partial Differential Equation (PDE) techniques in wavelet based image processing to remove noise and reduce edge artifacts generated by wavelet thresholding. We employ a variational framework, in particular the minimization of total variation (TV), to select and modify the retained wavelet coefficients so that the reconstructed images have fewer oscillations near edges while noise is smoothed. Numerical experiments show that this approach improves the reconstructed image quality in wavelet compression and in denoising.

KW - Image processing

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KW - Wavelet

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Total variation wavelet thresholding

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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