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Sparsity Optimization in Design of Multidimensional Filter Networks
Linköping University, Department of Biomedical Engineering. Linköping University, The Institute of Technology. (Medical Informatics)
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.ORCID iD: 0000-0003-1836-4200
Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology. (Optimization)
2013 (English)Report (Other academic)
Abstract [en]

Filter networks is a powerful tool used for reducing the image processing time, while maintaining its reasonably high quality.They are composed of sparse sub-filters whose low sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. If to disregard the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers. Each of the local minimizers is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2013. , 21 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2013:16
Keyword [en]
Sparse optimization; Cardinality Constraint; Multicriteria Optimization; Multilinear Least-Squares Problem; Filter networks; Medical imaging
National Category
Computational Mathematics Medical Image Processing Signal Processing
Identifiers
URN: urn:nbn:se:liu:diva-103915ISRN: LiTH-MAT-R-2013/16-SEOAI: oai:DiVA.org:liu-103915DiVA: diva2:692904
Available from: 2014-02-03 Created: 2014-02-03 Last updated: 2016-11-24Bibliographically approved
In thesis
1. Large-Scale Optimization Methods with Application to Design of Filter Networks
Open this publication in new window or tab >>Large-Scale Optimization Methods with Application to Design of Filter Networks
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Nowadays, large-scale optimization problems are among those most challenging. Any progress in developing methods for large-scale optimization results in solving important applied problems more effectively. Limited memory methods and trust-region methods represent two ecient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the efficiency of the former approach, especially in the case of large-scale problems. For this reason, the limited memory methods are usually combined with a line search. We develop new limited memory trust-region algorithms for large-scale unconstrained optimization. They are competitive with the traditional limited memory line-search algorithms.

In this thesis, we consider applied optimization problems originating from the design of lter networks. Filter networks represent an ecient tool in medical image processing. It is based on replacing a set of dense multidimensional lters by a network of smaller sparse lters called sub-filters. This allows for improving image processing time, while maintaining image quality and the robustness of image processing.

Design of lter networks is a nontrivial procedure that involves three steps: 1) choosing the network structure, 2) choosing the sparsity pattern of each sub-filter and 3) optimizing the nonzero coecient values. So far, steps 1 and 2 were mainly based on the individual expertise of network designers and their intuition. Given a sparsity pattern, the choice of the coecients at stage 3 is related to solving a weighted nonlinear least-squares problem. Even in the case of sequentially connected lters, the resulting problem is of a multilinear least-squares (MLLS) type, which is a non-convex large-scale optimization problem. This is a very dicult global optimization problem that may have a large number of local minima, and each of them is singular and non-isolated. It is characterized by a large number of decision variables, especially for 3D and 4D lters.

We develop an effective global optimization approach to solving the MLLS problem that reduces signicantly the computational time. Furthermore, we  develop efficient methods for optimizing sparsity of individual sub-filters  in lter networks of a more general structure. This approach offers practitioners a means of nding a proper trade-o between the image processing quality and time. It allows also for improving the network structure, which makes automated some stages of designing lter networks.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2014. 52 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1561
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-103646 (URN)10.3384/diss.diva-103646 (DOI)978-91-7519-456-1 (ISBN)
Public defence
2014-02-26, Nobel (BL32), B-huset, Campus Valla, Linköping University, Linköping, 13:15 (English)
Opponent
Supervisors
Available from: 2014-02-03 Created: 2014-01-21 Last updated: 2015-06-02Bibliographically approved

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Sparsity Optimization in Design of Multidimensional Filter Networks (revised version)(1212 kB)128 downloads
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Andersson, MatsBurdakov, OlegKnutsson, HansZikrin, Spartak

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