Denoising of $B_z$ data for conductivity reconstruction in magnetic resonance electrical impedance tomography (MREIT)

Abstract

This thesis proposes effective PDE-based denoising techniques for magnetic resonance electrical impedance tomography (MREIT). MREIT is an imaging tool which provides cross-sectional conductivity images of a target object. If we inject currents to a target object, MREIT measures the induced magnetic flux density $B_z$ and reconstructs conductivity images. Due to the fact that this tool utilizes the derivative information of $B_z$, the data quality is significant in the reconstruction. However in $\it{in vivo}$ experiments and medical applications to humans, the measured $B_z$ has low SNR since we cannot use high magnitude currents. Furthermore the $B_z$ has salt-pepper type noise in outer layers of bones and gas-filled organs. Hence the reconstructed conductivity will not be reliable without the effective denoising. We propose modifications of the Lee-Hahn method for denoising $B_z$. The Lee-Hahn method is remarkable in its ability to remove noise from normal images, however, modifications are necessary for applications to $B_z$ due to the data properties; the data is microscale and the ramp structure is very weak. The proposed modifications enable us to perform isotropic smoothing in salt-pepper type noisy regions which are identified through eigenvalue analysis while we use anisotropic smoothing for preserving ramp structure in the other regions. We confirm that the modified Lee-Hahn method performs effectively in noise removal from $B_z$ through evaluations using three different noisy data sets: a simulated phantom, an experimental phantom, and a post-mortem canine brain.