Automated Parameter Selection for Total Variation Minimization in Image Restoration

Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an L τ -data fidelity term, τ ∈ { 1 , 2 } , are presented. The automated selection of the regularization parameter is based on the discrepancy principle, whereby in each iterat...

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Bibliographic Details
Published inJournal of mathematical imaging and vision Vol. 57; no. 2; pp. 239 - 268
Main Author Langer, Andreas
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2017
Springer Nature B.V
Subjects
Algorithms
Applications of Mathematics
Automation
Computer Science
Image Processing and Computer Vision
Image restoration
Iterative methods
Mathematical Methods in Physics
Mathematical models
Noise reduction
Optimization
Regularization
Signal,Image and Speech Processing
Impulse noise
Constrained/unconstrained problem
Discrepancy principle
Gaussian noise
Locally dependent regularization parameter
Automated parameter selection
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Summary:Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an L τ -data fidelity term, τ ∈ { 1 , 2 } , are presented. The automated selection of the regularization parameter is based on the discrepancy principle, whereby in each iteration a total variation model has to be minimized. In the case of a locally varying parameter, this amounts to solve a multiscale total variation minimization problem. For solving the constituted multiscale total variation model, convergent first- and second-order methods are introduced and analyzed. Numerical experiments for image denoising and image deblurring show the efficiency, the competitiveness, and the performance of the proposed fully automated scalar and locally varying parameter selection algorithms.
ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-016-0676-2