Research On Phase Retrieval Algorithm Based On Short-time Fourier Transform

The problem of phase retrieval is the reconstructed phase of the optical field from a given value of the optical field intensity distribution measurements.The phase retrieval algorithm is the core of phase retrieval technology and the key to the development and application of this technology.The phase retrieval problem,as a nonlinear measurement problem,is one of the more important research topics in the inverse problem.Optical sensors generally capture only the amplitude information of the light field,and the phase information is directly lost.The traditional optical transform system is Fourier transform,which cannot guarantee the uniqueness of signal recovery.While the short-time Fourier transform adds the window function to the Fourier transform,which can guarantee the uniqueness of recovery.This paper focuses on how to recover the original signal's phase based on the short-time Fourier measurement.(1)The phase retrieval problem from the short-time fractional Fourier transform is studied,and the short-time fractional Fourier transform is the generalization of the short-time Fourier transform.As an extension of the Fourier transforms in the time-frequency domain,the fractional Fourier transform can be measured from the short-time Fourier transform amplitude information under different rotation angles.Simulation experiments have demonstrated that a minimum of three orders should be selected to ensure signal recovery accuracy,the redundant information of the window function guarantees the uniqueness of phase retrieval,and the rectangle window is more effective the three window functions.(2)The non-convex phase retrieval problem is converted into a multi-objective convex optimization problem by introducing auxiliary variables,and then the multi-objective optimization problem is decomposed into multiple sub-problems for solutions using the alternating direction multiplier method.In this paper,a short-time Fourier transform phase retrieval algorithm based on the alternating direction multiplier method is designed.The convergence theorem of the algorithm is explored and the convergence of the algorithm is proved when certain conditions are satisfied.Simulation experiments show that the performance of the algorithm on one-dimensional signals and two-dimensional natural images is a good result of phase retrieval,respectively.The experimental simulation shows that the proposed algorithm has advantages in recovering the original signal from flexible windows.The algorithm is able to recover the original signal estimate with a small error,and the results show that the rectangular window functions improve accuracy of phase retrieval.(3)The representation of sparse signals under compressive sensing is studied.In this paper,an adaptive sparse basis is learned from a fixed sparse basis using transfer learning,and a transfer learning-based sparse signal optimization algorithm is proposed.The experimental results show that the algorithm can increase the incoherence of the sensing matrix,the original signal can become more sparse by the optimized sparse basis transform,and the sparse signal recovery using the optimized matrix can improve the signal recovery accuracy.(4)The phase retrieval of sparse signals is obtained from the short-time Fourier transform.With transfer learning optimization as the objective function and the data fidelity term in the phase retrieval problem as the regularization term,the multi-objective optimization model for sparse phase retrieval is established.The sparsity of the signal is the a priori condition,and the short-time Fourier transform is used to introduce redundant information.The Sparse STFT algorithm is proposed to guarantee the accuracy and uniqueness of phase retrieval.The experimental results show that the algorithm has a small-time complexity and a high recovery accuracy.