Sparsity-undersampling tradeoff of compressed sensing in the complex domain

In this paper, recently developed ONE-L1 algorithms for compressed sensing are applied to complex-valued signals and sampling matrices. The optimal and iterative solution of ONE-L1 algorithms enables empirical investigation and evaluation of the sparsity-undersampling tradeoff of ℓ1 minimization of complex-valued signals. A remarkable finding is that, not only there exists a sharp phase transition for the complex case determining the behavior of the sparsity-undersampling tradeoff, but also this phase transition is different and superior to that for the real case, providing a significantly improved success phase in the transition plane.