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The Multidimensional Circulant Rational Covariance Extension Problem: Solutions and Applications in Image Compression
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-9778-1426
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0001-5158-9255
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. Shanghai Jiao Tong University, China.ORCID iD: 0000-0002-2681-8383
2016 (English)In: 2015 54th IEEE Conference on Decision and Control (CDC), 2015, Institute of Electrical and Electronics Engineers (IEEE), 2016, 5320-5327 p.Conference paper (Refereed)
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
Institute of Electrical and Electronics Engineers (IEEE), 2016. 5320-5327 p.
Series
Proceedings of the IEEE Conference on Decision and Control, ISSN 0743-1546 ; 2016
Keyword [en]
approximation theory, cepstral analysis, covariance analysis, data compression, entropy, image coding, method of moments, rational functions, approximation procedure, cepstral matching, circulant trigonometric moment problems, image compression, moment integral, multidimensional circulant rational covariance extension problem, multidimensional spectrum domain, rational functions, simultaneous covariance, spectra identification, weighted entropy functionals, Convex functions, Entropy, Image coding, Inverse problems, Optimization
National Category
Robotics Signal Processing Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-197632DOI: 10.1109/CDC.2015.7403052ISI: 000381554505083ScopusID: 2-s2.0-84962034240ISBN: 978-147997886-1 OAI: oai:DiVA.org:kth-197632DiVA: diva2:1052239
Conference
54th IEEE Conference on Decision and Control, CDC 2015, Osaka International Convention Center (Grand Cube)5-3-51 Nakanoshima, Kita-KuOsaka, Japan, 15 December 2015 through 18 December 2015
Funder
Swedish Research Council, 2014-5870Swedish Foundation for Strategic Research , AM13-0049
Note

QC 20161206

Available from: 2016-12-05 Created: 2016-12-05 Last updated: 2016-12-20Bibliographically approved

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