Complex Successive Concave Sparsity Approximation

In this paper we extend the successive concave sparsity approximation (SCSA) algorithm to complex numbers in order to make it available for applications benefiting of it e.g. radar applications. SCSA is an attractive reconstruction algorithm for compressive sensing (CS) problems due to its high reconstruction performance (superior to ℓ₁ algorithms) and in particular since it does not require any “hard” parameters, unlike all hard thresholding (HT) algorithms, which may be unknown in radar applications. We call this extended version complex successive concave sparsity approximation (CSCSA) and evaluate its performance by use of phase transition plots for random and discrete Fourier transform (DFT) sensing operators and further compare it with the two well known algorithms normalized iterative hard thresholding (NIHT) and fast iterative shrinkage-thresholding algorithm (FISTA), where we especially show how the reconstruction performance of NIHT declines in case of wrongly assumed parameters.