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Sparsity Optimization in Design of Multidimensional Filter Networks
Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV). (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.ORCID iD: 0000-0002-9091-4724
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology. (Optimization)
2015 (English)In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 16, no 2, 259-277 p.Article in journal (Refereed) Published
Abstract [en]

Filter networks are used as a powerful tool used for reducing the image processing time and maintaining high image quality.They are composed of sparse sub-filters whose high 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. Even when disregarding the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers, each of which 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
Springer, 2015. Vol. 16, no 2, 259-277 p.
Keyword [en]
Sparse optimization; Cardinality Constraint; Multicriteria Optimization; Multilinear Least-Squares Problem; Filter networks; Medical imaging
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-115788DOI: 10.1007/s11081-015-9280-3ISI: 000358253700001OAI: oai:DiVA.org:liu-115788DiVA: diva2:796663
Available from: 2015-03-19 Created: 2015-03-19 Last updated: 2017-12-04Bibliographically approved

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Andersson, MatsBurdakov, OlegKnutsson, HansZikrin, Spartak

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