Single Shot Phase Retrieval Algorithm Based On Structural Sparsity In Gradient Domain

The key issue in phase imaging is phase retrieval.Phase retrieval refers to the problem of recovering the original image from magnitude information via linear transform.In this work,we study the near field phase retrieval algorithm based on single shot phase imaging with a coded aperture.Due to the loss of the phase information,the problem is ill-posed.In this paper,based on the sparse representation,we focus on the phase retrieval algorithm using the total variation and the overlapping structural sparsity.The main contents are as follows:First,considering that there are two fresnel diffraction in the single shot phase imaging with a coded aperture,we improve the two step single shot phase retrieval algorithm using the total variation of the amplitude and the phase of the complex amplitude.This method divides the phase retrieval process into two steps,in the first step,HIO is exploited to recover the complex amplitude behind the mask,and the second step is a compressed sensing progress which uses the total variation of the amplitude and the phase as the regularization term.And two methods are utilized to solve the second step.The experiment results indicate the effectiveness of the algorithm.Secondly,we treat the two fresnel diffraction in the SPICA imaging model as a whole.Taking advantage of the total variation of the ampitude and pahse,we proposed the single shot phase retrieval algorithm based on the total variation.Then we get the partial derivatives of the discrete total variation.The steepest descent method is used to solve the corresponding optimization problem.The experimental results show that the proposed algorithm outperforms the reference algorithms obviously.Finally,considering the fact that the total variation of image is easy to produce staircase effect,we propose a single shot phase retrieval algorithm based on structural sparsity.The proposed algorithm exploits the overlapping structural sparsity of the total variation,and represents the structural sparsity in the form of convolution,making the problem easy to solve.The experiment results show that the complex amplitude can be reconstructed from noisy diffraction pattern using the proposed algorithm.