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Title

On phase transition of compressed sensing in the complex domain

Author(s)

Yang, Zai;  Zhang, Cishen;  Xie, Lihua

Abstract

The phase transition is a performance measure of the sparsity-undersampling tradeoff in compressed sensing (CS). This letter reports our first observation and evaluation of an empirical phase transition of the $ell_{1}$ minimization approach to the complex valued CS (CVCS), which is positioned well above the known phase transition of the real valued CS in the phase plane. This result can be considered as an extension of the existing phase transition theory of the block-sparse CS (BSCS) based on the universality argument, since the CVCS problem does not meet the condition required by the phase transition theory of BSCS but its observed phase transition coincides with that of BSCS. Our result is obtained by applying the recently developed ONE-L1 algorithms to the empirical evaluation of the phase transition of CVCS.

Publication type

Journal article

Research centre

Swinburne University of Technology. Faculty of Engineering and Industrial Sciences

Source

IEEE Signal Processing Letters, Vol. 19, no. 1 (Jan 2012), pp. 47-50

Publication year

2012

FOR Code(s)

0906 Electrical and Electronic Engineering

Keyword(s)

Complex signals;  Compressed sensing;  Joint sparsity;  Minimization;  ONE-L1 algorithms;  Phase transition

Publisher

IEEE

ISSN

1070-9908

Publisher URL

http://dx.doi.org/10.1109/lsp.2011.2177496

Copyright

Copyright © 2011 IEEE. The accepted manuscript is reproduced in accordance with the copyright policy of the publisher. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

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