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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 University, 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, 1950-1982 p.Article 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
Society for Industrial and Applied Mathematics Publications , 2016. Vol. 54, no 4, 1950-1982 p.
Keyword [en]
Convex optimization, Covariance extension, Generalized entropy, Image compression, Multidimensional spectral estimation, Trigonometric moment problem, Estimation, Image processing, Signal processing, Spectrum analysis, Generalized entropies, Moment problems, One dimensional problems, Rational covariance extension problem, Signal and image processing, Signal processing technique, Spectral Estimation, Inverse problems
National Category
Robotics Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-195469DOI: 10.1137/15M1043236ISI: 000385011200006ScopusID: 2-s2.0-84984666883OAI: oai:DiVA.org:kth-195469DiVA: diva2:1050196
Funder
Swedish Research Council
Note

QC 20161128

Available from: 2016-11-28 Created: 2016-11-03 Last updated: 2016-11-28Bibliographically approved

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