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Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport
Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden..
Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0001-5158-9255
2018 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 20, p. 5285-5298Article in journal (Refereed) Published
Abstract [en]

In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal mass transport problem in the spectral domain. This may then be interpreted in the covariance domain, suggesting a natural way of interpolating and extrapolating Toeplitz matrices, such that the positive semidefiniteness and the Toeplitz structure of these matrices are preserved. The proposed distance measure is also shown to be contractive with respect to both additive and multiplicative noise and thereby allows for a quantification of the decreased distance between signals when these are corrupted by noise. Finally, we illustrate how this approach can be used for several applications in signal processing. In particular, we consider interpolation and extrapolation of Toeplitz matrices, as well as clustering problems and tracking of slowly varying stochastic processes.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC , 2018. Vol. 66, no 20, p. 5285-5298
Keywords [en]
Covariance interpolation, optimal mass transport, Toeplitz matrices, spectral estimation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-235558DOI: 10.1109/TSP.2018.2866432ISI: 000444825200006Scopus ID: 2-s2.0-85052704347OAI: oai:DiVA.org:kth-235558DiVA, id: diva2:1252504
Note

QC 20181002

Available from: 2018-10-02 Created: 2018-10-02 Last updated: 2018-10-02Bibliographically approved

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Karlsson, Johan

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