Study Of Robust Phase Retrieval Algorithm Based On Sparse Representation

Phase retrieval refers to the problem of recovering the original image from magnitude-only of its Fourier transform, or of any other linear transform. Due to the loss of phase information, this problem is ill-posed. In practice, the phase retrieval problems are corrupted with different noise. Therefore this paper focuses on robust phase retrieval algorithms based on sparse representation, the specific contents are as follows:Firstly, considering that the random phase illumination applied to phase retrieval problems can reduce the sampling ratio and the time complexity, a resistance to poisson noise pollution phase retrieval algorithm based on random phase illumination is proposed. The negative-log poisson likehood function is used for data fidelity term and the total variation regularization term which constrains the the gradient transform sparse of the image is introduced in the proposed algorithm. Experimental results show that the proposed algorithm can achieve better image reconstruction quality for the phase retrieval problems corrupted with different poisson noise levels.Secondly, considering that different types of noise interferences exist in the phase retrieval problems in practical applications, a robust phase retrieval algorithm based total variation regularization term is proposed. Not only the total variation regularization term but also the fidelity term which contains the weighted sum of l1-norm and l2-norm is utilized in the method. Experimental results show that for different types of noises and mixed noise the proposed algorithm is robust without any prior knowledge of the noise distribution.Finally, considering that most of the images contain different image components, a robust phase retrieval algorithm based on two-step image reconstruction is proposed. This method divides the phase retrieval process into two steps: contour retrieval and detail retrieval. The first step the alternating direction method of multipliers method is exploited to solve the optimization problem of incorporating the total variation regularization term, which results in retrieving the contour of the image. In order to ensure that the reconstructed image contains rich details, the reconstructed image obtained in the first step is used as a coarse estimate of the original image for the second step. Also the Fourier magnitudes and the sparsity of the image under the dual-tree complex wavelet transform are adopted to reconstruct the details of the image. Experimental results show that the proposed algorithm provides high image quality with different types of noises.