The Research Of Phase Retrieval Algorithm Based On Image Sparse Representation And Nonliner Compressed Sensing

The problem of phase retrieval, namely, is 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. Many kinds of regularizations are widely used on image processing algorithm, including sparse regularization, total variation regularization. In this paper, based on the framework of nonlinear compressive sensing, using prior knowledge to complete the research of phase retrieval. The main contents are as follows:Firstly, the sparsity prior is the precondition of image reconstruction, according to different sparsity measures, including lp-norm, ln-norm and group sparsity. We proposed different phase retrieval algorithms based on different sparse regularization for sparse signal. At last, verify the effectiveness of the proposed algorithm through experiments.Secondly, based on the framework of nonlinear compressive sensing, we proposed a novel phase retrieval algorithm which exploits the sparsity of the natural images under the image gradient operator. The algorithm incorporates the total variation regularization into the phase retrieval problem, which based on support constraints and amplitude constraints. Moreover, the 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.Finally, take advantage of that total generalized variation can improve the ladder effects caused in first order total variation, we proposed a phase retrieval algorithm based on the total generalized variation regularization. In the absence of support information, using the ADMM algorithm to optimize the problem. Reflect the effectiveness of the algorithm through the experiments with many images.