Performance Analysis and Implementation of Hybrid Conjugate Gradient Method in Electromagnetic Tomography

Abstract

Electromagnetic tomography (EMT) is a type of electrical tomography based on electromagnetic induction. Reconstructing images with EMT involves solving inverse problems, which are often poorly defined due to limited prior information about imaging features. Optimization methods such as conjugate gradient (CG), Quasi-Newton, and Steepest Descent can help minimize these problems. The conjugate gradient (CG) algorithm is an iterative method that efficiently handles equations with multiple inputs, saving time but requiring more memory. In this research, four hybrid CG methods which is MN-LAMR, MN-FR, MN-LS and MN-PRP are used to reduce the number of iterations (NOI) and CPU time, achieving excellent numerical performance. Based on numerical performances, MN-LAMR is the best method. Then, MN-LAMR is implemented into the EMT system to produce a new system called EMT-CG. The efficiency of the EMT and EMT-CG systems is evaluated based on error analysis using root mean square error (RMSE). The implementation of MN-LAMR into EMT improves its system efficiency according to the smaller number RMSE in comparison between EMT and EMT-CG. The findings highlight the hybrid CG method's capability within the EMT system which will be useful in enhancing the medical field technology.