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

The sensitivity distribution of the electromagnetic tomography (EMT) system based on tunneling magnetoresistance (TMR) is quite different from the traditional coil measurement EMT system due to the change of detection sensor. The sensitivity of the TMRs-EMT system is higher only near the TMR sensors but lower at other locations in the region of interest, which results in a more serious ill-conditioned problem of image reconstruction. Focusing on the ill-conditioned problem, the Landweber algorithm is optimized by using an appropriate weight and an appropriate relaxation strategy in this article. By verifying the consistency of variation of the spectral radius of the iterative matrix and variation of condition number for the Landweber method, a new weight matrix is introduced for the general Landweber method to reduce the condition number. On this basis, an optimal relaxation factor is determined based on the principle of minimizing the spectral radius of the newly derived iterative matrix. By comparing the imaging results of the new method with the Landweber with a relaxation factor of 1, it can be seen that the average correlation coefficient with the new approach for the five models used in this article is 0.8466, which is much higher than 0.7633 of the Landweber with a relaxation factor of 1. Meanwhile, the proposed method has a faster imaging speed. The convergence analysis of the two methods shows that the new relaxation factor determination strategy can overcome the semiconvergence problem of Landweber.