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MULTIDIMENSIONAL RATIONAL COVARIANCE EXTENSION WITH APPLICATIONS TO SPECTRAL ESTIMATION AND 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 Univ, Dept Automat & Math, Shanghai 200240, Peoples R China..ORCID iD: 0000-0002-2681-8383
2016 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 54, no 4, p. 1950-1982Article in journal (Refereed) Published
Abstract [en]

The rational covariance extension problem (RCEP) is an important problem in systems and control occurring in such diverse fields as control, estimation, system identification, and signal and image processing, leading to many fundamental theoretical questions. In fact, this inverse problem is a key component in many identification and signal processing techniques and plays a fundamental role in prediction, analysis, and modeling of systems and signals. It is well known that the RCEP can be reformulated as a (truncated) trigonometric moment problem subject to a rationality condition. In this paper we consider the more general multidimensional trigonometric moment problem with a similar rationality constraint. This generalization creates many interesting new mathematical questions and also provides new insights into the original one-dimensional problem. A key concept in this approach is the complete smooth parameterization of all solutions, allowing solutions to be tuned to satisfy additional design specifications without violating the complexity constraints. As an illustration of the potential of this approach we apply our results to multidimensional spectral estimation and image compression. This is just a first step in this direction, and we expect that more elaborate tuning strategies will enhance our procedures in the future.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS , 2016. Vol. 54, no 4, p. 1950-1982
Keywords [en]
covariance extension, trigonometric moment problem, convex optimization, generalized entropy, multidimensional spectral estimation, image compression
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-242737DOI: 10.1137/15M1043236ISI: 000385011200006Scopus ID: 2-s2.0-84984666883OAI: oai:DiVA.org:kth-242737DiVA, id: diva2:1290007
Note

QC 20190219

Available from: 2019-02-19 Created: 2019-02-19 Last updated: 2019-08-21Bibliographically approved

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Ringh, AxelKarlsson, JohanLindquist, Anders

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