Blind deconvolution of covariance matrix inverses for autoregressive processes

Golyandina, Nina and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2020. Blind deconvolution of covariance matrix inverses for autoregressive processes. Linear Algebra and its Applications 593 , pp. 188-211. 10.1016/j.laa.2020.02.005

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Abstract

Matrix C can be blindly deconvoluted if there exist matrices A and B such that C = A * B, where * denotes the operation of matrix convolution. We study the prob- lem of matrix deconvolution in the case where matrix C is proportional to the inverse of the autocovariance matrix of an autoregressive process. We show that the deconvolution of such matrices is important in problems of Hankel structured low-rank approximation (HSLRA). In the cases of autoregressive models of orders one and two, we fully charac- terize the range of parameters where such deconvolution can be performed and provide construction schemes for performing deconvolutions. We also consider general autoregres- sive models of order p, where we prove that the deconvolution C = A * B does not exist if the matrix B is diagonal and its size is larger than p.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0024-3795
Funders:	no
Date of First Compliant Deposit:	26 February 2020
Date of Acceptance:	5 February 2020
Last Modified:	23 Nov 2024 10:45
URI:	https://orca.cardiff.ac.uk/id/eprint/129987

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