Study On A Sequential Subspace Optimization Acceleration Algorithm For Solving Nonlinear Inverse Problems

In recent years,as an emerging interdisciplinary subject,inverse problems have been increasingly applied in industrial design,medical imaging,signal detection,etc.,which has caused extensive attention and in-depth research by experts in mathematics,physics,engineering technology and other fields.In solving numerical physics equations,the purpose of the inverse problem is to determine some unknown factors in the equation,such as coefficient,right term,solution condition and domain,etc.,based on the known information of the solution part.The inverse problem is usually ill-posed,which brings great difficulties to the solution.Iterative regularization is one of the effective methods for solving ill-posed problems.In order to solve ill-posed problems,a fast two-point gradient iterative regularization method for Hilbert/Banach space nonlinear inverse problem is proposed and analyzed in this paper.This algorithm is based on sequence Bregman projection and has uniformly convex penalty terms.The penalty term can be non-smooth,including L1 and variational of the penalty term functional to reconstruct the sparse and discontinuous features of the solution.Under the general assumption of iterative regularization method,the convergence analysis of the algorithm is given.The construction of two-point gradient method involves the selection of combination parameters,which is discussed systematically.Through the numerical simulation parameter identification,a reconstruction framework of TV mixed with L1 and L1mixed with L2 is proposed,which verifies the effectiveness of the method.Compared with the original sequence subspace algorithm and the two-point gradient algorithm in terms of reconstruction accuracy and convergence speed,the numerical results show that the algorithm significantly improves the acceleration effect and reconstruction accuracy compared with other classical algorithms.A new iterative regularization method is proposed by combining the sequence subspace method with the two-point gradient method,which optimizes the iteration format and improves the numerical effect.The selection of combination parameters changes the uniqueness of iterative sequence and improves the corresponding theoretical analysis of convergence.In practice,the scale of the problem is often very large,the algorithm with slow iteration speed is no longer applicable,The proposed fast iteration regularization method is more practical and more widely applied.