Hybrid spectrum conjugate gradient algorithm in electromagnetic tomography

Abstract

Electromagnetic tomography is a process detection technology based upon the principles of electromagnetic induction. The forward problem model and sensitivity distribution matrix of electromagnetic tomography are introduced as the basis of the inverse problem. The search direction and iterative parameters of the conjugate gradient algorithm are modified to improve the quality and convergence of image reconstruction. A new spectral parameter conjugate gradient algorithm is described to modify the search direction, which is used to control the angle between the old and new search directions. The search direction is determined according to the iteration of each step in order to find the optimal solution. Combining the advantages of the Fletcher-Reeves and Polak-Ribiere-Polyak algorithms in the nonlinear conjugate gradient algorithm, they are mixed in a specific proportion to obtain a new hybrid conjugate gradient algorithm. In order to verify the effectiveness of the modified conjugate gradient algorithm, three physical models of electromagnetic tomography system are constructed, and the modified conjugate gradient algorithm is compared with the traditional algorithm. The experimental results show that the reconstructed image quality of the modified spectral conjugate gradient algorithm is higher and has better numerical performance. The hybrid conjugate gradient algorithm highlights the advantages of the Fletcher-Reeves and Polak-Ribiere-Polyaks algorithms. The convergence speed is faster than the Polak-Ribiere-Polyak method, and the imaging quality is higher than the other algorithms.