Analysis of the Singular Values for Conductivity Reconstruction in Magneto-Acoustic Tomography With Magnetic Induction

Abstract

Due to the acoustic source distribution and limited bandwidth ultrasound measurement, the dominant ultrasound signals always come from the boundary of the electrical conductivity in magneto-acoustic tomography with magnetic induction (MAT-MI). To make full use of the strong boundary ultrasound signals, a system matrix is built which shows the relationship between the electrical conductivity and the ultrasound signals. By analyzing the singular values of the system matrix, the necessary signal to noise ratio(SNR) level is estimated in this study. An inverse procedure based on the truncated singular value decomposition(TSVD) method is presented to improve the quality of the reconstructed MAT-MI image. Simulation results show that the reconstructed conductivity images by using the new algorithm match better than that of the back-projection algorithm. Both the simulation results and the experiment results prove the reconstructed image is close to the original conductivity distribution when the more singular values are used in the inverse procedure. Meanwhile, as the number of singular values increases, the effect of noise will be enhanced in the reconstructed image. The proposed reconstruction algorithm can improve the quality of the reconstruction image for a low SNR system. Moreover, the system matrix based reconstruction algorithm proposed in this work will help to analyze the physical process and to obtain accurate high-resolution reconstructions for MAT-MI.

Keywords

• Magneto acoustic tomography with magnetic induction
• singular values decomposition
• system matrix
• inverse problem
• electrical conductivity