Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems
SIAM Journal on Matrix Analysis and Applications
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection
International Journal of Computer Vision
Selection of regularisation parameters for total variation denoising
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 03
SSIAI '08 Proceedings of the 2008 IEEE Southwest Symposium on Image Analysis and Interpretation
Estimation of optimal PDE-based denoising in the SNR sense
IEEE Transactions on Image Processing
Parameter Estimation in TV Image Restoration Using Variational Distribution Approximation
IEEE Transactions on Image Processing
Fast parameter sensitivity analysis of PDE-based image processing methods
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VII
Variational structure-texture image decomposition on manifolds
Signal Processing
Total variation regularization algorithms for images corrupted with different noise models: a review
Journal of Electrical and Computer Engineering
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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.