Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport

Elvander, FilipLund 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. (författare)

QC 20181002
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.

Jakobsson, AndreasLund 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.(Swepub:lu)mats-aaj (författare)
Karlsson, JohanKTH,KTH Royal Institute of Technology,Optimeringslära och systemteori(Swepub:kth)u1yx87ls (författare)
Statistical Signal Processing GroupForskargrupper vid Lunds universitet (creator_code:org_t)

Ingår i:IEEE Transactions on Signal Processing: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC66:20, s. 5285-52981053-587X1941-0476

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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