To enable prefect reconstruction of the magnitude and phase of the complex images in the coded diffraction imaging system

many coded diffraction patterns are required

which leads to time consuming of the sampling process.To reduce the number of coded diffraction patterns

a robust phase retrieval algorithm which exploits the statistical characteristic of the higher-order Markov random fields is proposed based on the nonlinear compressed sensing framework.The presented method regularizes the magnitude and phase separately

and combines the data fidelity term with the regularization terms of the magnitude and phase to formulate the cost function.Moreover

the heavy-ball algorithm is utilized for solving the corresponding non-convex optimization problem.Experimental results show that the proposed method can achieve high image quality with fewer coded diffraction patterns

and is robust to noise.