| A fast multilevel algorithm for wavelet-regularized image restoration. | |
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MedLine Citation:
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PMID: 19188124 Owner: NLM Status: MEDLINE |
Abstract/OtherAbstract:
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We present a multilevel extension of the popular "thresholded Landweber" algorithm for wavelet-regularized image restoration that yields an order of magnitude speed improvement over the standard fixed-scale implementation. The method is generic and targeted towards large-scale linear inverse problems, such as 3-D deconvolution microscopy. The algorithm is derived within the framework of bound optimization. The key idea is to successively update the coefficients in the various wavelet channels using fixed, subband-adapted iteration parameters (step sizes and threshold levels). The optimization problem is solved efficiently via a proper chaining of basic iteration modules. The higher level description of the algorithm is similar to that of a multigrid solver for PDEs, but there is one fundamental difference: the latter iterates though a sequence of multiresolution versions of the original problem, while, in our case, we cycle through the wavelet subspaces corresponding to the difference between successive approximations. This strategy is motivated by the special structure of the problem and the preconditioning properties of the wavelet representation. We establish that the solution of the restoration problem corresponds to a fixed point of our multilevel optimizer. We also provide experimental evidence that the improvement in convergence rate is essentially determined by the (unconstrained) linear part of the algorithm, irrespective of the type of wavelet. Finally, we illustrate the technique with some image deconvolution examples, including some real 3-D fluorescence microscopy data. |
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Authors:
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Cédric Vonesch; Michael Unser |
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Publication Detail:
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Type: Evaluation Studies; Journal Article; Research Support, Non-U.S. Gov't Date: 2009-02-02 |
Journal Detail:
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Title: IEEE transactions on image processing : a publication of the IEEE Signal Processing Society Volume: 18 ISSN: 1057-7149 ISO Abbreviation: IEEE Trans Image Process Publication Date: 2009 Mar |
Date Detail:
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Created Date: 2009-02-12 Completed Date: 2009-04-16 Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 9886191 Medline TA: IEEE Trans Image Process Country: United States |
Other Details:
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Languages: eng Pagination: 509-23 Citation Subset: IM |
Affiliation:
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Biomedical Imaging Group, EPFL, Lausanne, Switzerland. cedric.vonesch@epfl.ch |
Export Citation:
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| MeSH Terms | |
Descriptor/Qualifier:
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Algorithms* Artificial Intelligence* Image Enhancement / methods* Image Interpretation, Computer-Assisted / methods* Imaging, Three-Dimensional / methods* Microscopy, Fluorescence / methods* Pattern Recognition, Automated / methods* Reproducibility of Results Sensitivity and Specificity Signal Processing, Computer-Assisted |
From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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