Research On Acceleration And Parallelization Of Electromagnetic Inversion Algorithms

Electromagnetic inverse problem is to solve the inverse problem of reconstructing the geometry or electrical parameters of target scatterer by use of measured scattering field data and forward propagation model.It is widely used in nondestructive detection,microwave remote sensing,biomedical imaging and other fields.Electromagnetic inversion is an ill-posed nonlinear inverse problem.Aiming at the practical bottleneck of the current nonlinear inversion algorithm for large computation cost,how to reduce the computational cost and increase the convergence rate under the premise of ensuring the accuracy of inversion results? It has always been a hot issue in the research of inversion algorithm.In this paper,we mainly study the acceleration and parallelization of the electromagnetic inversion algorithm.Aiming at inexact Newton inversion algorithm based on threshold Landweber iteration(IN-LW)huge storage cost and computational cost,from two aspects of the inversion algorithm process acceleration and the GPU parallel framework,according to the sparse characteristics of Fréchet derivative matrix,we accelerate and parallelize electromagnetic inversion algorithm under the framework of inexact Newton method.First,based on the electromagnetic forward propagation model,a generalized nonlinear model of the electromagnetic inverse problem is proposed.Aiming at such a nonlinear ill-posed inverse problem,we use the inexact Newton method to explain the solution of internal iterative linear equations and the external iterative update process.The implementation process of the inexact Newton inversion algorithm based on the threshold Landweber iteration is described,and the storage and computation cost are analyzed.Secondly,starting from the derivation process of Fréchet derivative matrix,we describe the large scale sparse characteristics Fréchet derivative matrix.We put forward the sparse compression storage of Fréchet derivative matrix to reduce the storage cost of algorithm.At the same time,combined with the characteristics of stable fast convergence of LSQR algorithm for sparse linear systems,and the main calculation of LSQR algorithm is matrix vector multiplication,avoiding singular value decomposition and adjoint matrix solution in Landweber iteration,so the computing efficiency of internal linear equation solution is improved.Based on these two points,the IN-LSQR inversion algorithm is proposed for the acceleration of electromagnetic inversion process.Finally,combining the multi-threaded parallel computing capacity of GPU devices,to solve the linearize inversion problem,we analyzed the implementation process of FISTA algorithm,and propose parallel implementation of matrix vector multiplication and soft threshold operation in FISTA algorithm,FISTA-GPU algorithm has been confirmed to have a good speedup by comparison experiments.What's more,aiming at the nonlinear inversion problem,we use BiCG and BiCGSTAB algorithm to solve the internal sparse linear equation,and propose a parallel scheme for the core operation of sparse matrix vector multiplication.The speedup of IN-BiCG-GPU and INBiCGSTAB-GPU algorithm is compared and verified.