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  • 1.
    Andersson, Mats
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Global search strategies for solving multilinear least-squares problems2012Inngår i: Sultan Qaboos University Journal for Science, ISSN 1027-524X, Vol. 17, nr 1, s. 12-21Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by results of numerical experiments performed for some problems related to the design of filter networks.

  • 2.
    Andersson, Mats
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Global Search Strategies for Solving Multilinear Least-squares Problems2011Rapport (Annet vitenskapelig)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear least-squares problem. The difference is that a multilinearoperator is used in place of a matrix-vector product. The MLLS istypically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows formoving from one local minimizer to a better one. The efficiencyof this strategy isillustrated by results of numerical experiments performed forsome problems related to the design of filter networks.

  • 3.
    Andersson, Mats
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik. Linköpings universitet, Tekniska högskolan.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Sparsity Optimization in Design of Multidimensional Filter Networks2013Rapport (Annet vitenskapelig)
    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.

  • 4.
    Andersson, Mats
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Sparsity Optimization in Design of Multidimensional Filter Networks2015Inngår i: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 16, nr 2, s. 259-277Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 5.
    Burdakov, Oleg
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Gong, Lujin
    Samsung Advanced Institute of Technology, China Lab, Beijing, China.
    Yuan, Ya-Xiang
    State Key Laboratory of Scientic and Engineering Computing, Institute of Computational.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    On Efficiently Combining Limited Memory and Trust-Region Techniques2013Rapport (Annet vitenskapelig)
    Abstract [en]

    Limited memory quasi-Newton methods and trust-region methods represent two efficient 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 show how to efficiently combine limited memory and trust-region techniques. One of our approaches is based on the eigenvalue decomposition of the limited memory quasi-Newton approximation of the Hessian matrix. The decomposition allows for finding a nearly-exact solution to the trust-region subproblem defined by the Euclidean norm with an insignificant computational overhead compared with the cost of computing the quasi-Newton direction in line-search limited memory methods. The other approach is based on two new eigenvalue-based norms. The advantage of the new norms is that the trust-region subproblem is separable and each of the smaller subproblems is easy to solve. We show that our eigenvalue-based limited-memory trust-region methods are globally convergent. Moreover, we propose improved versions of the existing limited-memory trust-region algorithms. The presented results of numerical experiments demonstrate the efficiency of our approach which is competitive with line-search versions of the L-BFGS method.

  • 6.
    Burdakov, Oleg
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Gong, Lujin
    Tencent, Beijing, China.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Yuan, Ya-xiang
    State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS, Beijing, China.
    On Efficiently Combining Limited-Memory and Trust-Region Techniques2017Inngår i: Mathematical Programming Computation, ISSN 1867-2949, E-ISSN 1867-2957, Vol. 9, nr 1, s. 101-134Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Limited-memory quasi-Newton methods and trust-region methods represent two efficient 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 show how to efficiently combine limited-memory and trust-region techniques. One of our approaches is based on the eigenvalue decomposition of the limited-memory quasi-Newton approximation of the Hessian matrix. The decomposition allows for finding a nearly-exact solution to the trust-region subproblem defined by the Euclidean norm with an insignificant computational overhead as compared with the cost of computing the quasi-Newton direction in line-search limited-memory methods. The other approach is based on two new eigenvalue-based norms. The advantage of the new norms is that the trust-region subproblem is separable and each of the smaller subproblems is easy to solve. We show that our eigenvalue-based limited-memory trust-region methods are globally convergent. Moreover, we propose improved versions of the existing limited-memory trust-region algorithms. The presented results of numerical experiments demonstrate the efficiency of our approach which is competitive with line-search versions of the L-BFGS method.

  • 7.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Large-Scale Optimization Methods with Application to Design of Filter Networks2014Doktoravhandling, med artikler (Annet vitenskapelig)
    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.

    Delarbeid
    1. On Efficiently Combining Limited Memory and Trust-Region Techniques
    Åpne denne publikasjonen i ny fane eller vindu >>On Efficiently Combining Limited Memory and Trust-Region Techniques
    2013 (engelsk)Rapport (Annet vitenskapelig)
    Abstract [en]

    Limited memory quasi-Newton methods and trust-region methods represent two efficient 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 show how to efficiently combine limited memory and trust-region techniques. One of our approaches is based on the eigenvalue decomposition of the limited memory quasi-Newton approximation of the Hessian matrix. The decomposition allows for finding a nearly-exact solution to the trust-region subproblem defined by the Euclidean norm with an insignificant computational overhead compared with the cost of computing the quasi-Newton direction in line-search limited memory methods. The other approach is based on two new eigenvalue-based norms. The advantage of the new norms is that the trust-region subproblem is separable and each of the smaller subproblems is easy to solve. We show that our eigenvalue-based limited-memory trust-region methods are globally convergent. Moreover, we propose improved versions of the existing limited-memory trust-region algorithms. The presented results of numerical experiments demonstrate the efficiency of our approach which is competitive with line-search versions of the L-BFGS method.

    sted, utgiver, år, opplag, sider
    Linköping: Linköping University Electronic Press, 2013. s. 33
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2013:13
    Emneord
    Unconstrained Optimization; Large-scale Problems; Limited Memory Methods;
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-102005 (URN)LiTH-MAT-R--2013/13--SE (ISRN)
    Tilgjengelig fra: 2013-11-26 Laget: 2013-11-26 Sist oppdatert: 2016-01-12bibliografisk kontrollert
    2. Global search strategies for solving multilinear least-squares problems
    Åpne denne publikasjonen i ny fane eller vindu >>Global search strategies for solving multilinear least-squares problems
    2012 (engelsk)Inngår i: Sultan Qaboos University Journal for Science, ISSN 1027-524X, Vol. 17, nr 1, s. 12-21Artikkel i tidsskrift (Fagfellevurdert) Published
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by results of numerical experiments performed for some problems related to the design of filter networks.

    sted, utgiver, år, opplag, sider
    Sultan Qaboos University, 2012
    Emneord
    Global optimization; Global search strategies; Multilinear least-squares; Filter
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-78918 (URN)
    Tilgjengelig fra: 2012-08-28 Laget: 2012-06-25 Sist oppdatert: 2015-09-03bibliografisk kontrollert
    3. Sparsity Optimization in Design of Multidimensional Filter Networks
    Åpne denne publikasjonen i ny fane eller vindu >>Sparsity Optimization in Design of Multidimensional Filter Networks
    2013 (engelsk)Rapport (Annet vitenskapelig)
    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.

    sted, utgiver, år, opplag, sider
    Linköping: Linköping University Electronic Press, 2013. s. 21
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2013:16
    Emneord
    Sparse optimization; Cardinality Constraint; Multicriteria Optimization; Multilinear Least-Squares Problem; Filter networks; Medical imaging
    HSV kategori
    Identifikatorer
    urn:nbn:se:liu:diva-103915 (URN)LiTH-MAT-R-2013/16-SE (ISRN)
    Tilgjengelig fra: 2014-02-03 Laget: 2014-02-03 Sist oppdatert: 2016-11-24bibliografisk kontrollert
1 - 7 of 7
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  • Annet format
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