Two Effective Strategies for Complex Domain Compressive Sensing

In this paper, we propose two novel recovery schemes for complex domain compressive sensing. Firstly, we present a new strategy to separate the real and imaginary parts of a complex signal for $$\ell _{1}$$ minimization. While the method is simple, simulation results show that it is quite efficient because it reduces the sampling rate. Secondly, the least squares (LS) sub-problem is a key part of the orthogonal matching pursuit (OMP) algorithm and accounts for a large part of the computational load. We employ the Landweber algorithm to efficiently solve the LS problem. Furthermore, we propose four new parameter options to accelerate the convergence. Our numerical experiments show that our method is competitive with the pseudo-inverse.