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UPRE method for total variation parameter selection

Authors:

Brendt Wohlberg,

Hongbin GuoAuthors Info & Claims

Signal Processing, Volume 90, Issue 8

Pages 2546 - 2551

https://doi.org/10.1016/j.sigpro.2010.02.025

Published: 01 August 2010 Publication History

Abstract

Total variation (TV) regularization is a popular method for solving a wide variety of inverse problems in image processing. In order to optimize the reconstructed image, it is important to choose a good regularization parameter. The unbiased predictive risk estimator (UPRE) has been shown to give a good estimate of this parameter for Tikhonov regularization. In this paper we propose an extension of the UPRE method to the TV problem. Since direct computation of the extended UPRE is impractical in the case of inverse problems such as deblurring, due to the large scale of the associated linear problem, we also propose a method which provides a good approximation of this large scale problem, while significantly reducing computational requirements.

References

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Cited By

Cascarano PFranchini GKobler EPorta FSebastiani A(2023)Constrained and unconstrained deep image prior optimization models with automatic regularizationComputational Optimization and Applications10.1007/s10589-022-00392-w84:1(125-149)Online publication date: 1-Jan-2023
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Gong MJiang XLi H(2017)Optimization methods for regularization-based ill-posed problemsFrontiers of Computer Science: Selected Publications from Chinese Universities10.1007/s11704-016-5552-011:3(362-391)Online publication date: 1-Jun-2017
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Information

Published In

cover image Signal Processing

Signal Processing Volume 90, Issue 8

August, 2010

303 pages

ISSN:0165-1684

Issue’s Table of Contents

Copyright © Elsevier B.V. © 2010.

Publisher

Elsevier North-Holland, Inc.

United States

Publication History

Published: 01 August 2010

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Cited By

Cascarano PFranchini GKobler EPorta FSebastiani A(2023)Constrained and unconstrained deep image prior optimization models with automatic regularizationComputational Optimization and Applications10.1007/s10589-022-00392-w84:1(125-149)Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1007/s10589-022-00392-w
Yang XZhang JLiu YZheng XLiu K(2018)Super-resolution image reconstruction using fractional-order total variation and adaptive regularization parametersThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-018-1570-235:12(1755-1768)Online publication date: 3-Jul-2018
https://dl.acm.org/doi/10.1007/s00371-018-1570-2
Gong MJiang XLi H(2017)Optimization methods for regularization-based ill-posed problemsFrontiers of Computer Science: Selected Publications from Chinese Universities10.1007/s11704-016-5552-011:3(362-391)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.1007/s11704-016-5552-0
Langer A(2017)Automated Parameter Selection for Total Variation Minimization in Image RestorationJournal of Mathematical Imaging and Vision10.1007/s10851-016-0676-257:2(239-268)Online publication date: 1-Feb-2017
https://dl.acm.org/doi/10.1007/s10851-016-0676-2
Shi MHan TLiu S(2016)Total variation image restoration using hyper-Laplacian prior with overlapping group sparsitySignal Processing10.1016/j.sigpro.2015.11.022126:C(65-76)Online publication date: 1-Sep-2016
https://dl.acm.org/doi/10.1016/j.sigpro.2015.11.022
Hacini MHachouf FDjemal K(2014)A new speckle filtering method for ultrasound images based on a weighted multiplicative total variationSignal Processing10.1016/j.sigpro.2013.12.008103:C(214-229)Online publication date: 1-Oct-2014
https://dl.acm.org/doi/10.1016/j.sigpro.2013.12.008
Rodríguez P(2013)Total variation regularization algorithms for images corrupted with different noise modelsJournal of Electrical and Computer Engineering10.1155/2013/2170212013(10-10)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.1155/2013/217021
Wu XZheng JWu CCai Y(2013)Variational structure-texture image decomposition on manifoldsSignal Processing10.1016/j.sigpro.2013.01.01993:7(1773-1784)Online publication date: 1-Jul-2013
https://dl.acm.org/doi/10.1016/j.sigpro.2013.01.019
Pätz TPreusser T(2012)Fast parameter sensitivity analysis of PDE-based image processing methodsProceedings of the 12th European conference on Computer Vision - Volume Part VII10.1007/978-3-642-33786-4_11(140-153)Online publication date: 7-Oct-2012
https://dl.acm.org/doi/10.1007/978-3-642-33786-4_11
Zhou XZhou FBai X(undefined)Parameter estimation for LP regularized image deconvolution2015 IEEE International Conference on Image Processing (ICIP)10.1109/ICIP.2015.7351737(4892-4896)
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