Field Map Reconstruction in Magnetic Resonance Imaging Using Bayesian Estimation

Abstract

Field inhomogeneities in Magnetic Resonance Imaging (MRI) can cause blur or image distortion as they produce off-resonance frequency at each voxel. These effects can be corrected if an accurate field map is available. Field maps can be estimated starting from the phase of multiple complex MRI data sets. In this paper we present a technique based on statistical estimation in order to reconstruct a field map exploiting two or more scans. The proposed approach implements a Bayesian estimator in conjunction with the Graph Cuts optimization method. The effectiveness of the method has been proven on simulated and real data.

Optimal Configuration for Relaxation Times Estimation in Complex Spin Echo Imaging

“…The acquisition model reported in Equation (1), which is a solution to Bloch equations, assuming that T E is short with respect to T R , is related to the noise-free case and does not take into account the dependency on the static magnetic field, B . Considering noise, in the complex domain, the model becomes: $y=y_R+i{y}_I=f(\mathit{\theta })exp(i\varphi )+(n_R+i{n}_I)$where n R and n I are the real and imaginary parts of the noise samples, which are distributed as independent circularly Gaussian variables [22], and ϕ represents the angle of the complex data [23,24]. Thus, the statistical distributions of the real and imaginary parts of the acquired signal are: $f_{Y_R}(y_R)=\frac{1}{\sqrt{2\pi {\sigma }^2}}exp\left(-\frac{{\left(y_R-f(\mathit{\theta })cos(\varphi )\right)}^2}{2{\sigma }^2}\right)$ $f_{Y_I}(y_I)=\frac{1}{\sqrt{2\pi {\sigma }^2}}exp\left(-\frac{{\left(y_I-ffalse(\mathrm{bold-italic\theta }false)sinfalse(\varphi false)\right)}^2}{2{\sigma }^2}\right)$where σ 2 is the variance of real and imaginary noise components.…”

A new application of compressive sensing in MRI

“…After the application of inverse 2D Fourier transform, the image in the space domain is formed. 7,8 Let us consider a Spin Echo (SE) imaging sequence. In a noise free case, the amplitude of the recorded signal g related to a single voxel can be written as: 9…”

A Novel Statistical Approach for Brain MR Images Segmentation Based on Relaxation Times

“…The acquisition model reported in ( 1 ) is related to the noise-free case. Considering noise, in the complex domain the model becomes where n R and n I are the real and imaginary parts of the noise samples, which are distributed as independent circularly Gaussian variables [ 12 ], and ϕ represents the angle of the complex data [ 13 , 14 ].…”