Low-Rank Structured Covariance Matrix Estimation

The covariance matrix estimation problem is posed in both the Bayesian and frequentist settings as the solution of a maximum a posteriori (MAP) or maximum likelihood (ML) optimization, respectively, when the true covariance consists of a known (or bounded) noise floor and a low-rank component. Persy...

Full description

Saved in:
Bibliographic Details
Published in:IEEE signal processing letters 2019-05, Vol.26 (5), p.700-704
Main Authors: Shikhaliev, Azer P., Potter, Lee C., Chi, Yuejie
Format: Article
Language:English
Subjects:
Bayesian analysis
Bayesian MAP
Clutter
Covariance matrices
Covariance matrix
Economic models
Eigenvalues
Eigenvalues and eigenfunctions
Estimating techniques
Iterative methods
low rank
maximum likelihood
Maximum likelihood estimation
Optimization
persymmetry
Thermal noise
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c291t-915c9bd71aedcb4ff4ff94210d2fa4673995285365d887286dbdb5f43e9ca74f3
cites cdi_FETCH-LOGICAL-c291t-915c9bd71aedcb4ff4ff94210d2fa4673995285365d887286dbdb5f43e9ca74f3
container_end_page 704
container_issue 5
container_start_page 700
container_title IEEE signal processing letters
container_volume 26
creator Shikhaliev, Azer P.
Potter, Lee C.
Chi, Yuejie
description The covariance matrix estimation problem is posed in both the Bayesian and frequentist settings as the solution of a maximum a posteriori (MAP) or maximum likelihood (ML) optimization, respectively, when the true covariance consists of a known (or bounded) noise floor and a low-rank component. Persymmetric structure may also be assumed. The MAP and ML solutions with the non-convex rank constraint are shown to be a simple scalar thresholding of eigenvalues of a suitably translated and projected sample covariance matrix. No iterative optimization is required; therefore, the computation is suited to real-time applications. Our proof is short and elementary without resorting to the duality theory. Numerical results are presented to illustrate the improved estimation performance obtained by incorporating the structural constraints on the unknown covariance.
doi_str_mv 10.1109/LSP.2019.2906405
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1109_LSP_2019_2906405</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>8675477</ieee_id><sourcerecordid>2203405883</sourcerecordid><originalsourceid>FETCH-LOGICAL-c291t-915c9bd71aedcb4ff4ff94210d2fa4673995285365d887286dbdb5f43e9ca74f3</originalsourceid><addsrcrecordid>eNo9kMtLxDAQxoMouK7eBS8Fz10nryY5yrI-oKK4eg5pmkBXbdck9fHfm6WLMDBz-L6Zb34InWNYYAzqql4_LQhgtSAKKgb8AM0w57IktMKHeQYBpVIgj9FJjBsAkFjyGYJ6-C6fTf9WrFMYbRqDa4vl8GVCZ3rrigeTQvdTrGLqPkzqhv4UHXnzHt3Zvs_R683qZXlX1o-398vrurRE4VQqzK1qWoGNa23DvM-lGMHQEm9YJahSnEhOK95KKYis2qZtuGfUKWsE83SOLqe92zB8ji4mvRnG0OeTmhCg-UMpaVbBpLJhiDE4r7chBw2_GoPecdGZi95x0Xsu2XIxWTrn3L9cVoIzIegfwQ9dcw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2203405883</pqid></control><display><type>article</type><title>Low-Rank Structured Covariance Matrix Estimation</title><source>IEEE Xplore (Online service)</source><creator>Shikhaliev, Azer P. ; Potter, Lee C. ; Chi, Yuejie</creator><creatorcontrib>Shikhaliev, Azer P. ; Potter, Lee C. ; Chi, Yuejie</creatorcontrib><description>The covariance matrix estimation problem is posed in both the Bayesian and frequentist settings as the solution of a maximum a posteriori (MAP) or maximum likelihood (ML) optimization, respectively, when the true covariance consists of a known (or bounded) noise floor and a low-rank component. Persymmetric structure may also be assumed. The MAP and ML solutions with the non-convex rank constraint are shown to be a simple scalar thresholding of eigenvalues of a suitably translated and projected sample covariance matrix. No iterative optimization is required; therefore, the computation is suited to real-time applications. Our proof is short and elementary without resorting to the duality theory. Numerical results are presented to illustrate the improved estimation performance obtained by incorporating the structural constraints on the unknown covariance.</description><identifier>ISSN: 1070-9908</identifier><identifier>EISSN: 1558-2361</identifier><identifier>DOI: 10.1109/LSP.2019.2906405</identifier><identifier>CODEN: ISPLEM</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Bayesian analysis ; Bayesian MAP ; Clutter ; Covariance matrices ; Covariance matrix ; Economic models ; Eigenvalues ; Eigenvalues and eigenfunctions ; Estimating techniques ; Iterative methods ; low rank ; maximum likelihood ; Maximum likelihood estimation ; Optimization ; persymmetry ; Thermal noise</subject><ispartof>IEEE signal processing letters, 2019-05, Vol.26 (5), p.700-704</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c291t-915c9bd71aedcb4ff4ff94210d2fa4673995285365d887286dbdb5f43e9ca74f3</citedby><cites>FETCH-LOGICAL-c291t-915c9bd71aedcb4ff4ff94210d2fa4673995285365d887286dbdb5f43e9ca74f3</cites><orcidid>0000-0002-6766-5459 ; 0000-0002-1537-1627</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/8675477$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,54796</link.rule.ids></links><search><creatorcontrib>Shikhaliev, Azer P.</creatorcontrib><creatorcontrib>Potter, Lee C.</creatorcontrib><creatorcontrib>Chi, Yuejie</creatorcontrib><title>Low-Rank Structured Covariance Matrix Estimation</title><title>IEEE signal processing letters</title><addtitle>LSP</addtitle><description>The covariance matrix estimation problem is posed in both the Bayesian and frequentist settings as the solution of a maximum a posteriori (MAP) or maximum likelihood (ML) optimization, respectively, when the true covariance consists of a known (or bounded) noise floor and a low-rank component. Persymmetric structure may also be assumed. The MAP and ML solutions with the non-convex rank constraint are shown to be a simple scalar thresholding of eigenvalues of a suitably translated and projected sample covariance matrix. No iterative optimization is required; therefore, the computation is suited to real-time applications. Our proof is short and elementary without resorting to the duality theory. Numerical results are presented to illustrate the improved estimation performance obtained by incorporating the structural constraints on the unknown covariance.</description><subject>Bayesian analysis</subject><subject>Bayesian MAP</subject><subject>Clutter</subject><subject>Covariance matrices</subject><subject>Covariance matrix</subject><subject>Economic models</subject><subject>Eigenvalues</subject><subject>Eigenvalues and eigenfunctions</subject><subject>Estimating techniques</subject><subject>Iterative methods</subject><subject>low rank</subject><subject>maximum likelihood</subject><subject>Maximum likelihood estimation</subject><subject>Optimization</subject><subject>persymmetry</subject><subject>Thermal noise</subject><issn>1070-9908</issn><issn>1558-2361</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNo9kMtLxDAQxoMouK7eBS8Fz10nryY5yrI-oKK4eg5pmkBXbdck9fHfm6WLMDBz-L6Zb34InWNYYAzqql4_LQhgtSAKKgb8AM0w57IktMKHeQYBpVIgj9FJjBsAkFjyGYJ6-C6fTf9WrFMYbRqDa4vl8GVCZ3rrigeTQvdTrGLqPkzqhv4UHXnzHt3Zvs_R683qZXlX1o-398vrurRE4VQqzK1qWoGNa23DvM-lGMHQEm9YJahSnEhOK95KKYis2qZtuGfUKWsE83SOLqe92zB8ji4mvRnG0OeTmhCg-UMpaVbBpLJhiDE4r7chBw2_GoPecdGZi95x0Xsu2XIxWTrn3L9cVoIzIegfwQ9dcw</recordid><startdate>20190501</startdate><enddate>20190501</enddate><creator>Shikhaliev, Azer P.</creator><creator>Potter, Lee C.</creator><creator>Chi, Yuejie</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-6766-5459</orcidid><orcidid>https://orcid.org/0000-0002-1537-1627</orcidid></search><sort><creationdate>20190501</creationdate><title>Low-Rank Structured Covariance Matrix Estimation</title><author>Shikhaliev, Azer P. ; Potter, Lee C. ; Chi, Yuejie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c291t-915c9bd71aedcb4ff4ff94210d2fa4673995285365d887286dbdb5f43e9ca74f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Bayesian analysis</topic><topic>Bayesian MAP</topic><topic>Clutter</topic><topic>Covariance matrices</topic><topic>Covariance matrix</topic><topic>Economic models</topic><topic>Eigenvalues</topic><topic>Eigenvalues and eigenfunctions</topic><topic>Estimating techniques</topic><topic>Iterative methods</topic><topic>low rank</topic><topic>maximum likelihood</topic><topic>Maximum likelihood estimation</topic><topic>Optimization</topic><topic>persymmetry</topic><topic>Thermal noise</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shikhaliev, Azer P.</creatorcontrib><creatorcontrib>Potter, Lee C.</creatorcontrib><creatorcontrib>Chi, Yuejie</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Xplore</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics &amp; Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE signal processing letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shikhaliev, Azer P.</au><au>Potter, Lee C.</au><au>Chi, Yuejie</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Low-Rank Structured Covariance Matrix Estimation</atitle><jtitle>IEEE signal processing letters</jtitle><stitle>LSP</stitle><date>2019-05-01</date><risdate>2019</risdate><volume>26</volume><issue>5</issue><spage>700</spage><epage>704</epage><pages>700-704</pages><issn>1070-9908</issn><eissn>1558-2361</eissn><coden>ISPLEM</coden><abstract>The covariance matrix estimation problem is posed in both the Bayesian and frequentist settings as the solution of a maximum a posteriori (MAP) or maximum likelihood (ML) optimization, respectively, when the true covariance consists of a known (or bounded) noise floor and a low-rank component. Persymmetric structure may also be assumed. The MAP and ML solutions with the non-convex rank constraint are shown to be a simple scalar thresholding of eigenvalues of a suitably translated and projected sample covariance matrix. No iterative optimization is required; therefore, the computation is suited to real-time applications. Our proof is short and elementary without resorting to the duality theory. Numerical results are presented to illustrate the improved estimation performance obtained by incorporating the structural constraints on the unknown covariance.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/LSP.2019.2906405</doi><tpages>5</tpages><orcidid>https://orcid.org/0000-0002-6766-5459</orcidid><orcidid>https://orcid.org/0000-0002-1537-1627</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 1070-9908
ispartof IEEE signal processing letters, 2019-05, Vol.26 (5), p.700-704
issn 1070-9908
1558-2361
language eng
recordid cdi_crossref_primary_10_1109_LSP_2019_2906405
source IEEE Xplore (Online service)
subjects Bayesian analysis
Bayesian MAP
Clutter
Covariance matrices
Covariance matrix
Economic models
Eigenvalues
Eigenvalues and eigenfunctions
Estimating techniques
Iterative methods
low rank
maximum likelihood
Maximum likelihood estimation
Optimization
persymmetry
Thermal noise
title Low-Rank Structured Covariance Matrix Estimation
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T19%3A04%3A25IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Low-Rank%20Structured%20Covariance%20Matrix%20Estimation&rft.jtitle=IEEE%20signal%20processing%20letters&rft.au=Shikhaliev,%20Azer%20P.&rft.date=2019-05-01&rft.volume=26&rft.issue=5&rft.spage=700&rft.epage=704&rft.pages=700-704&rft.issn=1070-9908&rft.eissn=1558-2361&rft.coden=ISPLEM&rft_id=info:doi/10.1109/LSP.2019.2906405&rft_dat=%3Cproquest_cross%3E2203405883%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c291t-915c9bd71aedcb4ff4ff94210d2fa4673995285365d887286dbdb5f43e9ca74f3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2203405883&rft_id=info:pmid/&rft_ieee_id=8675477&rfr_iscdi=true