Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport

Elvander, Filip (författare): Lund University,Lunds universitet,Statistical Signal Processing Group,Forskargrupper vid Lunds universitet,Matematisk statistik,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Lund University Research Groups,Mathematical Statistics,Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH,Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden.

Jakobsson, Andreas (författare): Lund University,Lunds universitet,Statistical Signal Processing Group,Forskargrupper vid Lunds universitet,Matematisk statistik,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Lund University Research Groups,Mathematical Statistics,Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH,Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden.

Karlsson, Johan (författare): KTH,KTH Royal Institute of Technology,Optimeringslära och systemteori

(creator_code:org_t)

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2018
2018
Engelska 14 s.
Ingår i: IEEE Transactions on Signal Processing. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 1053-587X .- 1941-0476. ; 66:20, s. 5285-5298

Relaterad länk:: http://dx.doi.org/10...; visa fler...; https://lup.lub.lu.s...; https://doi.org/10.1...; https://urn.kb.se/re...; visa färre...

Abstract Ämnesord

Stäng

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 semi-definiteness 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.

TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Signalbehandling (hsv//swe)
ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Signal Processing (hsv//eng)
NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
NATURVETENSKAP -- Matematik (hsv//swe)
NATURAL SCIENCES -- Mathematics (hsv//eng)

Av författaren/redakt...: Elvander, Filip; Jakobsson, Andre ...; Karlsson, Johan

Om ämnet

TEKNIK OCH TEKNOLOGIER: TEKNIK OCH TEKNO ...; och Elektroteknik oc ...; och Signalbehandling

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