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An Extended Block Restricted Isometry Property for Sparse Recovery with Non-Gaussian Noise
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Mathematical Statistics)ORCID iD: 0000-0001-5673-620x
2018 (English)Conference paper, Poster (with or without abstract) (Refereed)
Abstract [en]

Recovering an unknown signal from significantly fewer measurements is a fundamental aspect in computational sciences today. The key ingredient is the sparsity of the unknown signal, a realisation that that has led to the theory of compressed censing, through which successful recovery of high dimensional (approximately) sparse signals is now possible at a rate significantly lower than the Nyquist sampling rate. Today, an interesting challenge lies in customizing the recovery process to take into account prior knowledge about e.g. signal structure and properties of present noise. We study recovery conditions for block sparse signal reconstruction from compressed measurements when partial support information is available via weighted mixed l2/lp minimization. We show theoretically that the extended block restricted isometry property can ensure robust recovery when the data fidelity constraint is expressed in terms of an lq norm of the residual error. Thereby, we also establish a setting wherein we are not restricted to a Gaussian measurement noise. The results are illustrated with a series of numerical experiments.

Place, publisher, year, edition, pages
2018.
Keywords [en]
Compressive sensing, block restricted isometry property, sparse recovery, non-Gaussian noise
National Category
Probability Theory and Statistics Signal Processing Medical Image Processing
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-154629OAI: oai:DiVA.org:umu-154629DiVA, id: diva2:1273280
Conference
COMPSTAT 2018, Iasi, Romania, August 28-31, 2018
Projects
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment
Funder
Swedish Research Council, 340-2013-534Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2020-03-03Bibliographically approved

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Leffler, KlaraZhou, ZhiyongYu, Jun

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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  • de-DE
  • en-GB
  • en-US
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  • nn-NO
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Output format
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