Research On Fast Phase Recovery Algorithm Based On Majorization-Minimization Optimization Framework

Phase recovery means that the original signal is recovered only from the amplitude of the measured signal or the intensity value of the measured signal without phase information.Phase recovery has a wide range of applications in the physical and engineering fields.Phase recovery is a non-convex inversion problem due to the loss of phase information.In response to this problem,it is proposed to perform signal recovery based on semi-definite programming techniques,but due to the increase of signal dimension in the matrix lifting process,such algorithms are not suitable for large-scale problems.The Wirtinger Flow algorithm uses the gradient descent method to recover the original signal from the signal strength measurement,but the algorithm has a slow convergence rate and relatively poor performance.The traditional Gerchberg-Saxton algorithm uses alternating iterative minimization to recover the original signal from the amplitude of the measured signal,but it is easy to fall into the local optimal solution.The recently proposed phase recovery algorithm based on the MM?Majorization–Minimization?framework has a slow convergence rate and the application of the algorithm is limited.Aiming at the above problems,this paper analyzes the advantages and disadvantages of several existing algorithms from the perspective of non-sparse and sparse signals.Combined with optimization theory,three fast iterative phase recovery algorithms based on MM optimization framework are proposed.This paper first proposes two fast phase recovery algorithms based on quasi-Newton iteration.The two methods consider two non-convex phase recovery data models in the case where the number of signal measurements is greater than the signal dimension.First,the two non-convex phase recovery problems are converted into different simple optimization problems by using the MM optimization framework,and then a new quasi-Newton iteration method is used to solve the optimized phase recovery problem.The proposed algorithms effectively solve the problem that the non-convex phase recovery problem is easy to fall into the local minimum and the convergence speed of the existing algorithm is slow.The experimental results show that the proposed algorithms are superior to the existing methods in the success rate of signal recovery and the convergence rate of the proposed algorithm when the measurement matrix is gaussian random measurement matrix and guidance vector matrix.In the case where the number of signal measurements is less than the original signal dimension,we consider the undersampling phase recovery problem based on the ₁ norm.In this paper,a sparse signal phase recovery algorithm based on gradient iteration and a fast phase recovery algorithm based on Steffensen variable step size are proposed.Based on the C-PRIME?Compressive Phase retrieval via Majorization–Minimization technique?algorithm,this paper firstly proposes a sparse signal phase recovery algorithm based on gradient iteration by using gradient framework and regularization theory.The algorithm transforms the undersampling phase recovery problem based on ₁ norm into the optimization problem of least absolute shrinkage and selection operator form.In the solution process,the Lipschitz constant as the gradient step size in the sparse signal phase recovery algorithm based on gradient iteration is not easy to calculate in large-scale data.Therefore,this paper considers the use of adaptive step size.First,assigning a suitable effective initial value to the step,and then iteratively update the step size,so that the algorithm more meets the actual engineering requirements.Meanwhile,considering that the phase recovery algorithm for sparse signals based on gradient iteration is also an algorithm based on MM optimization framework,and its convergence speed is slow.This paper accelerates the algorithm by Steffensen iterative acceleration method.Compared with the existing algorithms,the experimental results show that the proposed fast phase recovery algorithm based on Steffensen variable step size has faster convergence speed and stronger noise suppression performance.