<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-03809877v2</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-24T19:57:15+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Local Geometry of Nonconvex Spike Deconvolution from Low-Pass Measurements</title>
            <author role="crp">
              <persName>
                <forename type="first">Maxime</forename>
                <surname>Ferreira Da Costa</surname>
              </persName>
              <email type="md5">f25a81fffd1bdfec59fc90bae2510081</email>
              <email type="domain">centralesupelec.fr</email>
              <ptr type="url" target="https://maximeferreira.github.io/"/>
              <idno type="idhal" notation="string">maxime-ferreiradacosta</idno>
              <idno type="idhal" notation="numeric">1173204</idno>
              <idno type="halauthorid" notation="string">2609101-1173204</idno>
              <idno type="ARXIV">https://arxiv.org/a/ferreiradacosta_m_1</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-0073-8825</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=wUZMIFMAAAAJ</idno>
              <affiliation ref="#struct-1051117"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Yuejie</forename>
                <surname>Chi</surname>
              </persName>
              <email type="md5">44b5f96f65a8cc14d5a7cf4ed61af9dc</email>
              <email type="domain">cmu.edu</email>
              <idno type="idhal" notation="numeric">1303018</idno>
              <idno type="halauthorid" notation="string">1836203-1303018</idno>
              <affiliation ref="#struct-67135"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Maxime</forename>
                <surname>Ferreira Da Costa</surname>
              </persName>
              <email type="md5">f25a81fffd1bdfec59fc90bae2510081</email>
              <email type="domain">centralesupelec.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2022-10-10 23:49:19</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2023-05-16 09:51:05</date>
              <date type="whenWritten">2022-10-10</date>
              <date type="whenModified">2024-07-16 11:56:03</date>
              <date type="whenReleased">2023-05-16 09:55:52</date>
              <date type="whenProduced">2023-03-30</date>
              <date type="whenEndEmbargoed">2023-04-26</date>
              <ref type="file" target="https://centralesupelec.hal.science/hal-03809877v2/document">
                <date notBefore="2023-04-26"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://centralesupelec.hal.science/hal-03809877v2/file/NoncvxSuperResolution.pdf" id="file-4082409-3568206">
                <date notBefore="2023-04-26"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2208.10073"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1328359">
                <persName>
                  <forename>Maxime</forename>
                  <surname>Ferreira Da Costa</surname>
                </persName>
                <email type="md5">f25a81fffd1bdfec59fc90bae2510081</email>
                <email type="domain">centralesupelec.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03809877</idno>
            <idno type="halUri">https://centralesupelec.hal.science/hal-03809877</idno>
            <idno type="halBibtex">ferreiradacosta:hal-03809877</idno>
            <idno type="halRefHtml">&lt;i&gt;IEEE Journal on Selected Areas in Information Theory&lt;/i&gt;, 2023, 4, pp.1-15. &lt;a target="_blank" href="https://dx.doi.org/10.1109/JSAIT.2023.3262689"&gt;&amp;#x27E8;10.1109/JSAIT.2023.3262689&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">IEEE Journal on Selected Areas in Information Theory, 2023, 4, pp.1-15. &amp;#x27E8;10.1109/JSAIT.2023.3262689&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://hal.science/licences/copyright/">Copyright - All rights reserved<ref corresp="#file-4082409-3568206"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="SUP_LSS">Laboratoire des Signaux et Systèmes</idno>
            <idno type="stamp" n="SUP_TELECOMS" corresp="SUP_LSS">Pôle Télécoms et Réseaux</idno>
            <idno type="stamp" n="CENTRALESUPELEC">Ecole CentraleSupélec</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="UNIVERSITE-PARIS-SACLAY" corresp="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="GS-COMPUTER-SCIENCE">Graduate School Computer Science</idno>
            <idno type="stamp" n="GS-SPORT-HUMAN-MOVEMENT">Graduate School Sport, Mouvement, Facteurs Humains</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Local Geometry of Nonconvex Spike Deconvolution from Low-Pass Measurements</title>
                <author role="crp">
                  <persName>
                    <forename type="first">Maxime</forename>
                    <surname>Ferreira Da Costa</surname>
                  </persName>
                  <email type="md5">f25a81fffd1bdfec59fc90bae2510081</email>
                  <email type="domain">centralesupelec.fr</email>
                  <ptr type="url" target="https://maximeferreira.github.io/"/>
                  <idno type="idhal" notation="string">maxime-ferreiradacosta</idno>
                  <idno type="idhal" notation="numeric">1173204</idno>
                  <idno type="halauthorid" notation="string">2609101-1173204</idno>
                  <idno type="ARXIV">https://arxiv.org/a/ferreiradacosta_m_1</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-0073-8825</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=wUZMIFMAAAAJ</idno>
                  <affiliation ref="#struct-1051117"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Yuejie</forename>
                    <surname>Chi</surname>
                  </persName>
                  <email type="md5">44b5f96f65a8cc14d5a7cf4ed61af9dc</email>
                  <email type="domain">cmu.edu</email>
                  <idno type="idhal" notation="numeric">1303018</idno>
                  <idno type="halauthorid" notation="string">1836203-1303018</idno>
                  <affiliation ref="#struct-67135"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">168803</idno>
                <idno type="eissn">2641-8770</idno>
                <title level="j">IEEE Journal on Selected Areas in Information Theory</title>
                <imprint>
                  <publisher>IEEE</publisher>
                  <biblScope unit="volume">4</biblScope>
                  <biblScope unit="pp">1-15</biblScope>
                  <date type="datePub">2023-03-30</date>
                  <date type="dateEpub">2023-03-30</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2208.10073</idno>
              <idno type="doi">10.1109/JSAIT.2023.3262689</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Super-Resolution</term>
                <term xml:lang="en">Deconvolution</term>
                <term xml:lang="en">First Order Methods</term>
                <term xml:lang="en">Optimization</term>
              </keywords>
              <classCode scheme="https://dl.acm.org/ccs" n="ACM2012.B.1.0"/>
              <classCode scheme="https://dl.acm.org/ccs" n="ACM2012.G.3"/>
              <classCode scheme="https://dl.acm.org/ccs" n="ACM2012.G.4.0"/>
              <classCode scheme="halDomain" n="math.math-na">Mathematics [math]/Numerical Analysis [math.NA]</classCode>
              <classCode scheme="halDomain" n="info.info-it">Computer Science [cs]/Information Theory [cs.IT]</classCode>
              <classCode scheme="halDomain" n="spi.signal">Engineering Sciences [physics]/Signal and Image processing</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Spike deconvolution is the problem of recovering the point sources from their convolution with a known point spread function, which plays a fundamental role in many sensing and imaging applications. In this paper, we investigate the local geometry of recovering the parameters of point sources—including both amplitudes and locations—by minimizing a natural nonconvex least-squares loss function measuring the observation residuals. We propose preconditioned variants of gradient descent (GD), where the search direction is scaled via some carefully designed preconditioning matrices. We begin with a simple fixed preconditioner design, which adjusts the learning rates of the locations at a different scale from those of the amplitudes, and show it achieves a linear rate of convergence—in terms of entrywise errors—when initialized close to the ground truth, as long as the separation between the true spikes is sufficiently large. However, the convergence rate slows down significantly when the dynamic range of the source amplitudes is large. To bridge this issue, we introduce an adaptive preconditioner design, which compensates for the learning rates of different sources in an iteration-varying manner based on the current estimate. The adaptive design provably leads to an accelerated convergence rate that is independent of the dynamic range, highlighting the benefit of adaptive preconditioning in nonconvex spike deconvolution. Numerical experiments are provided to corroborate the theoretical findings.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-1051117" status="VALID">
          <idno type="IdRef">133818799</idno>
          <idno type="RNSR">199812842X</idno>
          <idno type="ROR">https://ror.org/00skw9v43</idno>
          <orgName>Laboratoire des signaux et systèmes</orgName>
          <orgName type="acronym">L2S</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.l2s.centralesupelec.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-411575" type="direct"/>
            <relation active="#struct-419361" type="direct"/>
            <relation name="UMR8506" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-67135" status="VALID">
          <orgName>Carnegie Mellon University [Pittsburgh]</orgName>
          <orgName type="acronym">CMU</orgName>
          <desc>
            <address>
              <addrLine>5000 Forbes Ave,  Pittsburgh, PA 15213</addrLine>
              <country key="US"/>
            </address>
            <ref type="url">http://www.cmu.edu/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-411575" status="VALID">
          <idno type="IdRef">184443237</idno>
          <idno type="ROR">https://ror.org/019tcpt25</idno>
          <orgName>CentraleSupélec</orgName>
          <desc>
            <address>
              <addrLine>3, rue Joliot Curie,Plateau de Moulon,91192 GIF-SUR-YVETTE Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.centralesupelec.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-419361" status="VALID">
          <idno type="IdRef">241345251</idno>
          <idno type="ROR">https://ror.org/03xjwb503</idno>
          <orgName>Université Paris-Saclay</orgName>
          <desc>
            <address>
              <addrLine>Bâtiment Bréguet, 3 Rue Joliot Curie 2e ét, 91190 Gif-sur-Yvette</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.universite-paris-saclay.fr/fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>