Journal article
Nonlocal regularization of inverse problems: a unified variational framework
IEEE transactions on image processing, Vol.22(8), pp.3192-3203
08/2013
DOI: 10.1109/TIP.2012.2216278
PMCID: PMC3969882
PMID: 23014745
Abstract
We introduce a unifying energy minimization framework for nonlocal regularization of inverse problems. In contrast to the weighted sum of square differences between image pixels used by current schemes, the proposed functional is an unweighted sum of inter-patch distances. We use robust distance metrics that promote the averaging of similar patches, while discouraging the averaging of dissimilar patches. We show that the first iteration of a majorize-minimize algorithm to minimize the proposed cost function is similar to current non-local methods. The reformulation thus provides a theoretical justification for the heuristic approach of iterating non-local schemes, which re-estimate the weights from the current image estimate. Thanks to the reformulation, we now understand that the widely reported alias amplification associated with iterative non-local methods are caused by the convergence to local minimum of the nonconvex penalty. We introduce an efficient continuation strategy to overcome this problem. The similarity of the proposed criterion to widely used non-quadratic penalties (eg. total variation and\n`\np\nsemi-norms) opens the door to the adaptation of fast algorithms developed in the context of compressive sensing; we introduce several novel algorithms to solve the proposed non-local optimization problem. Thanks to the unifying framework, these fast algorithms are readily applicable for a large class of distance metrics.
Details
- Title: Subtitle
- Nonlocal regularization of inverse problems: a unified variational framework
- Creators
- Zhili Yang - Department of Electrical and Computer Engineering, University of Rochester, NY, USAMathews Jacob - Department of Electrical and Computer Engineering, University of Iowa, IA, USA
- Resource Type
- Journal article
- Publication Details
- IEEE transactions on image processing, Vol.22(8), pp.3192-3203
- DOI
- 10.1109/TIP.2012.2216278
- PMID
- 23014745
- PMCID
- PMC3969882
- NLM abbreviation
- IEEE Trans Image Process
- ISSN
- 1057-7149
- eISSN
- 1941-0042
- Language
- English
- Date published
- 08/2013
- Academic Unit
- Roy J. Carver Department of Biomedical Engineering; Radiology; Electrical and Computer Engineering; Iowa Neuroscience Institute; Radiation Oncology
- Record Identifier
- 9984070961802771
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