On Phase Transition of Compressed Sensing in the Complex Domain

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.

4 pages, 3 figures

References in corpus (4)

• Sparsity and Incoherence in Compressive Sampling
• Off-grid Direction of Arrival Estimation Using Sparse Bayesian Inference
• Block-length dependent thresholds in block-sparse compressed sensing
• Orthonormal Expansion l1-Minimization Algorithms for Compressed Sensing

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• Asymptotic Analysis of Complex LASSO via Complex Approximate Message Passing (CAMP)
• Subsampling at Information Theoretically Optimal Rates