The problem of phase retrieval

namely

recovery of a signal only from the magnitude of its Fourier transform

or of any other linear transform.Due to the loss of phase information

this problem is ill-posed.Therefore

the prior knowledge is required to enable its accurate reconstruction.In this work

based on the framework of nonlinear compressive sensing

a novel phase retrieval algorithm which exploits the sparsity of the natural images under the image gradient operator is proposed.The algorithm incorporates the total variation regularization into the phase retrieval problem

which based on support constraints and amplitude constraints.Moreover

alternating direction method of multipliers (ADMM) is utilized for solving the corresponding non-convex optimization problem.Experimental results indicate that the performance of the proposed algorithm outperforms the classical algorithms

such as HIO

RAAR

moreover

it is robust to noise.