The Research Of Phase Retrieval Algorithm Based On Wavelet Sparsity And Total Variation Regularization

The essence of the phase retrieval technique is to reconstruct all the information of the signal by using the easily obtained intensity information,which can be realized by two ways of interference and diffraction.Among them,the diffraction method does not need to reference beam intervention,and the experimental device is simple,many scholars have carried on the key research to it.However,the traditional iterative diffraction method,such as the classical algorithm GS,HIO and so on,has slow convergence speed and easy to fall into stagnation.In order to improve the convergence speed and reconstruction accuracy,we use the priori knowledge of images as regularization,and put the coded diffraction pattern system to build the phase retrieval model,at last,we use iterative algorithm to solve this nonconvex optimization problem.The specific research contents are as follows:Firstly,the WF algorithm can reconstruct the image with only the gradient descent in the absence of noise under the coded diffraction model,but it needs many coded diffraction patterns.Based on the sparsity of the image in the wavelet domain,we proposed a phase retrieval algrithom that based on orthogonal wavelet transform.The experimental results show that the algorithm can reconstruct the image with only one coded diffraction pattern,and it has a certain anti-noise performance.Secondly,in view of the pseudo Gibbs distortion produced by the phase retrieval of orthogonal wavelet transform,we adopted the undecimated wavelet transform with good translation invariance,and all the sub-band after transformation are processed by total variation regularization.And then we construct the phase retrieval minimization model based on the undecimated wavelet and the total variation regularization,and use the alternating direction multiplier algorithm to solve the problem.The experimental results show that the image reconstruction quality can be improved by using two kinds of prior knowledge.Finally,we proposed a phase retrieval algorithm that fused multiple wavelet group sparsity and total variation regularization based on the diversity of orthogonal wavelet basis and the wavelet coefficients dependencies.We adopted composite splitting algorithm to solve this phase retrieval problem,and which decomposed the nonconvex problem into some sub-problems that can be solved easily.The algorithm we proposed reduced the reconstruction time compared with the state-of-the-art phase retrieval algorithms.The experimental results show that it has obvious advantages in the quality of image reconstruction and the time of reconstruction,and is robust to Gauss noise and Poisson noise.