PittsburghV1, Hal, Corpus, bibRecord, 000439

On unified view of nullspace-type conditions for recoveries associated with general sparsity structures

Identifieur interne : 000439 ( Hal/Corpus ); précédent : 000438; suivant : 000440

On unified view of nullspace-type conditions for recoveries associated with general sparsity structures

Auteurs : Anatoli Juditsky ; Fatma K L Nç Karzan ; Arkadii S. Nemirovski

Source :

Linear Algebra and its Applications [ 0024-3795 ] ; 2014-01-15.

RBID : Hal:hal-00978268

English descriptors

mix :
- Block-sparse recovery, Low-rank matrix recovery, Nuclear norm minimization, Nullspace property, Sparse recovery.

Abstract

We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity" and "usual l1 recovery," (b) block-sparsity with possibly overlapping blocks and associated block-l1 recovery, and (c) low-rank-oriented recovery by nuclear norm minimization. The proposed recovery routines are natural extensions of the usual l1 minimization used in Compressed Sensing. Specifically, within this framework, we present nullspace-type sufficient conditions for the recovery to be precise on sparse signals in the noiseless case. Then we derive error bounds for imperfect (nearly sparse signal, presence of observation noise, etc.) recovery under these conditions. In all of these cases, we present efficiently verifiable sufficient conditions for the validity of the associated nullspace properties.

Url:

https://hal.archives-ouvertes.fr/hal-00978268

DOI: 10.1016/j.laa.2013.07.025

Links to Exploration step

Hal:hal-00978268

Le document en format XML

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            <textClass>              <keywords scheme="author">                <term xml:lang="en">Nullspace property</term>
                <term xml:lang="en">Sparse recovery</term>
                <term xml:lang="en">Block-sparse recovery</term>
                <term xml:lang="en">Low-rank matrix recovery</term>
                <term xml:lang="en">Nuclear norm minimization</term>
              </keywords>
              <classCode scheme="classification">MSC: 15A83, 52A27, 68Q32, 90C25, 90C90</classCode>
              <classCode scheme="halDomain" n="math.math-st">Mathematics [math]/Statistics [math.ST]</classCode>
              <classCode scheme="halDomain" n="stat.th">Statistics [stat]/Statistics Theory [stat.TH]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity" and "usual l1 recovery," (b) block-sparsity with possibly overlapping blocks and associated block-l1 recovery, and (c) low-rank-oriented recovery by nuclear norm minimization. The proposed recovery routines are natural extensions of the usual l1 minimization used in Compressed Sensing. Specifically, within this framework, we present nullspace-type sufficient conditions for the recovery to be precise on sparse signals in the noiseless case. Then we derive error bounds for imperfect (nearly sparse signal, presence of observation noise, etc.) recovery under these conditions. In all of these cases, we present efficiently verifiable sufficient conditions for the validity of the associated nullspace properties.</abstract>
          </profileDesc>
        </hal>
</record>

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On unified view of nullspace-type conditions for recoveries associated with general sparsity structures

On unified view of nullspace-type conditions for recoveries associated with general sparsity structures

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