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Harmonic retrieval using weighted lifted-structure low-rank matrix completion
Electrical Engineering Department, Sharif University of Technology, Iran; Department of Electronic Systems, Aalborg university, Denmark.
KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Network and Systems Engineering. Electrical Engineering Department, Sharif University of Technology, Iran.ORCID iD: 0000-0003-4519-9204
Electrical and Computer Engineering Department, National Yang-Ming Chao-Tung University (NYCU), Taiwan.
Electrical Engineering Department, Sharif University of Technology, Iran.
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2024 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 216, article id 109253Article in journal (Refereed) Published
Abstract [en]

In this paper, we investigate the problem of recovering the frequency components of a mixture of K complex sinusoids from a random subset of N equally-spaced time-domain samples. Because of the random subset, the samples are effectively non-uniform. Besides, the frequency values of each of the K complex sinusoids are assumed to vary continuously within a given range. For this problem, we propose a two-step strategy: (i) we first lift the incomplete set of uniform samples (unavailable samples are treated as missing data) into a structured matrix with missing entries, which is potentially low-rank; then (ii) we complete the matrix using a weighted nuclear minimization problem. We call the method a weighted lifted-structured (WLi) low-rank matrix recovery. Our approach can be applied to a range of matrix structures such as Hankel and double-Hankel, among others, and provides improvement over the unweighted existing schemes such as EMaC and DEMaC. We provide theoretical guarantees for the proposed method, as well as numerical simulations in both noiseless and noisy settings. Both the theoretical and the numerical results confirm the superiority of the proposed approach.

Place, publisher, year, edition, pages
Elsevier BV , 2024. Vol. 216, article id 109253
Keywords [en]
Hankel structure, Lifting operator, Low-rank matrix completion
National Category
Signal Processing Control Engineering Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-339042DOI: 10.1016/j.sigpro.2023.109253Scopus ID: 2-s2.0-85174693122OAI: oai:DiVA.org:kth-339042DiVA, id: diva2:1815292
Note

QC 20231128

Available from: 2023-11-28 Created: 2023-11-28 Last updated: 2023-11-30Bibliographically approved

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Razavikia, Saeed

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