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Volume 2, Issue 4
Convex Variational Formulation with Smooth Coupling for Multicomponent Signal Decomposition and Recovery

Luis M. Briceño-Arias & Patrick L. Combettes

DOI: 10.4208/nmtma.2009.m9009s

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 485-508.

Published online: 2009-02

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  • Abstract

A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert spaces. The cost function consists of a separable term, in which each component is modeled through its own potential, and of a coupling term, in which constraints on linear transformations of the components are penalized with smooth functionals. An algorithm with guaranteed weak convergence to a solution to the problem is provided. Various multicomponent signal decomposition and recovery applications are discussed.

  • Keywords

Convex optimization, denoising, image restoration, proximal algorithm, signal decomposition, signal recovery.

  • AMS Subject Headings

94A12, 90C25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-485, author = {Luis M. Briceño-Arias and Patrick L. Combettes}, title = {Convex Variational Formulation with Smooth Coupling for Multicomponent Signal Decomposition and Recovery}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {4}, pages = {485--508}, abstract = {

A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert spaces. The cost function consists of a separable term, in which each component is modeled through its own potential, and of a coupling term, in which constraints on linear transformations of the components are penalized with smooth functionals. An algorithm with guaranteed weak convergence to a solution to the problem is provided. Various multicomponent signal decomposition and recovery applications are discussed.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2009.m9009s}, url = {http://global-sci.org/intro/article_detail/nmtma/6037.html} }
TY - JOUR T1 - Convex Variational Formulation with Smooth Coupling for Multicomponent Signal Decomposition and Recovery AU - Luis M. Briceño-Arias & Patrick L. Combettes JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 485 EP - 508 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/10.4208/nmtma.2009.m9009s UR - https://global-sci.org/intro/article_detail/nmtma/6037.html KW - Convex optimization, denoising, image restoration, proximal algorithm, signal decomposition, signal recovery. AB -

A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert spaces. The cost function consists of a separable term, in which each component is modeled through its own potential, and of a coupling term, in which constraints on linear transformations of the components are penalized with smooth functionals. An algorithm with guaranteed weak convergence to a solution to the problem is provided. Various multicomponent signal decomposition and recovery applications are discussed.

Luis M. Briceño-Arias and Patrick L. Combettes. (2009). Convex Variational Formulation with Smooth Coupling for Multicomponent Signal Decomposition and Recovery. Numerical Mathematics: Theory, Methods and Applications. 2 (4). 485-508. doi:10.4208/nmtma.2009.m9009s
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