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The multidimensional circulant rational covariance extension problem: Solutions and applications in image compression
KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2016 (English)In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2016, 5320-5327 p.Conference paper (Refereed)Text
Abstract [en]

Rational functions play a fundamental role in systems engineering for modelling, identification, and control applications. In this paper we extend the framework by Lindquist and Picci for obtaining such models from the circulant trigonometric moment problems, from the one-dimensional to the multidimensional setting in the sense that the spectrum domain is multidimensional. We consider solutions to weighted entropy functionals, and show that all rational solutions of certain bounded degree can be characterized by these. We also consider identification of spectra based on simultaneous covariance and cepstral matching, and apply this theory for image compression. This provides an approximation procedure for moment problems where the moment integral is over a multidimensional domain, and is also a step towards a realization theory for random fields.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2016. 5320-5327 p.
Keyword [en]
Convex functions, Entropy, Image coding, Indexes, Inverse problems, Optimization
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-188285DOI: 10.1109/CDC.2015.7403052ScopusID: 2-s2.0-84962034240ISBN: 9781479978861OAI: oai:DiVA.org:kth-188285DiVA: diva2:936783
Conference
54th IEEE Conference on Decision and Control, CDC 2015, 15 December 2015 through 18 December 2015
Note

QC 20160614

Available from: 2016-06-14 Created: 2016-06-09 Last updated: 2016-06-14Bibliographically approved

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Publisher's full textScopushttp://cdc2015.ieeecss.org/

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