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Sparsity optimization in design of multidimensional filter networks

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Abstract

Filter networks are a powerful tool for reducing 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 solving a sparse optimization problem where a cardinality constraint bounds below 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 the time 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.

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Acknowledgments

This work was supported by the Swedish Research Council; the Linnaeus Center for Control, Autonomy, and Decision-making in Complex Systems (CADICS); the Swedish Foundation for Strategic Research (SSF) Strategic Research Center (MOVIII); the Linköping University Center for Industrial Information Technology (CENIIT).

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Authors and Affiliations

  1. Department of Biomedical Engineering, Linköping University, 58185, Linköping, Sweden

    Mats Andersson & Hans Knutsson

  2. Department of Mathematics, Linköping University, 58183, Linköping, Sweden

    Oleg Burdakov & Spartak Zikrin

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  1. Mats Andersson
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  2. Oleg Burdakov
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  3. Hans Knutsson
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  4. Spartak Zikrin
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Correspondence to Oleg Burdakov.

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Andersson, M., Burdakov, O., Knutsson, H. et al. Sparsity optimization in design of multidimensional filter networks. Optim Eng 16, 259–277 (2015). https://doi.org/10.1007/s11081-015-9280-3

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  • DOI: https://doi.org/10.1007/s11081-015-9280-3

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