Filter networks are used as a powerful tool aimed at 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 solving a 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 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.
Technical Report LiTH-MAT-R-2013/16-SE, Department of Mathematics, Linkoping University, Linkoping, Sweden, 2013
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