Computer Science – Information Theory
Scientific paper
2011-09-11
IEEE Signal Processing Letters, vol. 19, no. 1, pp. 47--50, 2012
Computer Science
Information Theory
4 pages, 3 figures
Scientific paper
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.
Xie Lihua
Yang Zeping
Zhang Cishen
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