Volume 38, Issue 6
An Extended Block Restricted Isometry Property for Sparse Recovery with Non-Gaussian Noise

J. Comp. Math., 38 (2020), pp. 827-838.

Published online: 2020-06

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• Abstract

We study the recovery conditions of weighted mixed $\ell_2/\ell_p$ minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available. 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 $\ell_q$ norm of the residual error, thus establishing a setting wherein we are not restricted to Gaussian measurement noise. We illustrate the results with a series of numerical experiments.

• Keywords

Compressed sensing, block sparsity, partial support information, signal reconstruction, convex optimization.

94A12, 94A20

klara.leffler@umu.se (Klara Leffler)

zhiyongzhou@zucc.edu.cn (Zhiyong Zhou)

jun.yu@umu.se (Jun Yu)

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@Article{JCM-38-827, author = {Leffler , Klara and Zhou , Zhiyong and Yu , Jun }, title = {An Extended Block Restricted Isometry Property for Sparse Recovery with Non-Gaussian Noise}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {6}, pages = {827--838}, abstract = {

We study the recovery conditions of weighted mixed $\ell_2/\ell_p$ minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available. 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 $\ell_q$ norm of the residual error, thus establishing a setting wherein we are not restricted to Gaussian measurement noise. We illustrate the results with a series of numerical experiments.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1905-m2018-0256}, url = {http://global-sci.org/intro/article_detail/jcm/16969.html} }
TY - JOUR T1 - An Extended Block Restricted Isometry Property for Sparse Recovery with Non-Gaussian Noise AU - Leffler , Klara AU - Zhou , Zhiyong AU - Yu , Jun JO - Journal of Computational Mathematics VL - 6 SP - 827 EP - 838 PY - 2020 DA - 2020/06 SN - 38 DO - http://doi.org/10.4208/jcm.1905-m2018-0256 UR - https://global-sci.org/intro/article_detail/jcm/16969.html KW - Compressed sensing, block sparsity, partial support information, signal reconstruction, convex optimization. AB -

We study the recovery conditions of weighted mixed $\ell_2/\ell_p$ minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available. 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 $\ell_q$ norm of the residual error, thus establishing a setting wherein we are not restricted to Gaussian measurement noise. We illustrate the results with a series of numerical experiments.

Klara Leffler, Zhiyong Zhou & Jun Yu. (2020). An Extended Block Restricted Isometry Property for Sparse Recovery with Non-Gaussian Noise. Journal of Computational Mathematics. 38 (6). 827-838. doi:10.4208/jcm.1905-m2018-0256
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