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- Publisher Website: 10.1109/TSP.2019.2944740
- Scopus: eid_2-s2.0-85074191502
- WOS: WOS:000492996200004
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Article: TARM: A turbo-type algorithm for affine rank minimization
Title | TARM: A turbo-type algorithm for affine rank minimization |
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Authors | |
Keywords | affine rank minimization low-rank matrix denoising Low-rank matrix recovery matrix completion state evolution |
Issue Date | 2019 |
Citation | IEEE Transactions on Signal Processing, 2019, v. 67, n. 22, p. 5730-5745 How to Cite? |
Abstract | The affine rank minimization (ARM) problem arises in many real-world applications. The goal is to recover a low-rank matrix from a small amount of noisy affine measurements. The original problem is NP-hard, and so directly solving the problem is computationally prohibitive. Approximate low-complexity solutions for ARM have recently attracted much research interest. In this paper, we design an iterative algorithm for ARM based on message passing principles. The proposed algorithm is termed turbo-type ARM (TARM), as inspired by the recently developed turbo compressed sensing algorithm for sparse signal recovery. We show that, for right-orthogonally invariant linear (ROIL) operators, a scalar function called state evolution can be established to accurately predict the behaviour of the TARM algorithm. We also show that TARM converges faster than the counterpart algorithms when ROIL operators are used for low-rank matrix recovery. We further extend the TARM algorithm for matrix completion, where the measurement operator corresponds to a random selection matrix. Slight improvement of the matrix completion performance has been demonstrated for the TARM algorithm over the state-of-the-art algorithms. |
Persistent Identifier | http://hdl.handle.net/10722/327754 |
ISSN | 2023 Impact Factor: 4.6 2023 SCImago Journal Rankings: 2.520 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Xue, Zhipeng | - |
dc.contributor.author | Yuan, Xiaojun | - |
dc.contributor.author | Ma, Junjie | - |
dc.contributor.author | Ma, Yi | - |
dc.date.accessioned | 2023-05-08T02:26:35Z | - |
dc.date.available | 2023-05-08T02:26:35Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | IEEE Transactions on Signal Processing, 2019, v. 67, n. 22, p. 5730-5745 | - |
dc.identifier.issn | 1053-587X | - |
dc.identifier.uri | http://hdl.handle.net/10722/327754 | - |
dc.description.abstract | The affine rank minimization (ARM) problem arises in many real-world applications. The goal is to recover a low-rank matrix from a small amount of noisy affine measurements. The original problem is NP-hard, and so directly solving the problem is computationally prohibitive. Approximate low-complexity solutions for ARM have recently attracted much research interest. In this paper, we design an iterative algorithm for ARM based on message passing principles. The proposed algorithm is termed turbo-type ARM (TARM), as inspired by the recently developed turbo compressed sensing algorithm for sparse signal recovery. We show that, for right-orthogonally invariant linear (ROIL) operators, a scalar function called state evolution can be established to accurately predict the behaviour of the TARM algorithm. We also show that TARM converges faster than the counterpart algorithms when ROIL operators are used for low-rank matrix recovery. We further extend the TARM algorithm for matrix completion, where the measurement operator corresponds to a random selection matrix. Slight improvement of the matrix completion performance has been demonstrated for the TARM algorithm over the state-of-the-art algorithms. | - |
dc.language | eng | - |
dc.relation.ispartof | IEEE Transactions on Signal Processing | - |
dc.subject | affine rank minimization | - |
dc.subject | low-rank matrix denoising | - |
dc.subject | Low-rank matrix recovery | - |
dc.subject | matrix completion | - |
dc.subject | state evolution | - |
dc.title | TARM: A turbo-type algorithm for affine rank minimization | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1109/TSP.2019.2944740 | - |
dc.identifier.scopus | eid_2-s2.0-85074191502 | - |
dc.identifier.volume | 67 | - |
dc.identifier.issue | 22 | - |
dc.identifier.spage | 5730 | - |
dc.identifier.epage | 5745 | - |
dc.identifier.eissn | 1941-0476 | - |
dc.identifier.isi | WOS:000492996200004 | - |