An Ill-posed Optimization Method and Relaxation Strategy of Landweber for EMT System Based on TMR

Abstract

The sensitivity matrix of Electromagnetic Tomography (EMT) system based on Tunneling Magneto Resistance (TMR) has the characteristics of high sensitivity only near the TMR and low sensitivity at other positions, which leads to more serious ill-posed problem of image reconstruction. Focusing on the ill-posed problem, an appropriate weight matrix and relaxation strategy to optimize the Landweber method is proposed in this paper. By verifying the consistency of the condition number and spectral radius of iterative matrix, a weight matrix is introduced to improve the condition number. Then, based on the principle of minimizing the spectral radius of the newly derived iterative matrix, an optimal relaxation factor is determined for the optimized Landweber. Compared the new approach with Landweber with a constant relaxation factor 1, the results show that the average correlation coefficient (CC) of the optimized Landweber for the four models is 0.8260, which is much higher than the 0.6525 of Landweber with a constant relaxation factor. Meanwhile, the convergence analysis of the two algorithms indicates that the new approach can solve the semi-convergence problem of Landweber.