Spatially Regularized Multi-Exponential Transverse Relaxation Times Estimation from Magnitude Magnetic Resonance Images Under Rician Noise

Abstract

The extraction of multi-exponential decay parameters from multi-temporal images corrupted with Rician noise and with limited time samples proves to be a challenging problem frequently encountered in clinical and food MRI studies. This work aims at proposing a method for the estimation of multiexponential transverse relaxation times from noisy magnitude MRI images. A spatially regularized Maximum-Likelihood estimator accounting for the Rician distribution of the noise is introduced. To deal with the large-scale optimization problem, a Majoration-Minimization approach coupled with an adapted non-linear least squares algorithm is implemented. The proposed algorithm is numerically fast, stable and leads to accurate results. Its effectiveness is illustrated by an application to a simulated phantom and to magnitude multi spin echo MRI images acquired from a tomato sample.

Multi-Exponential Relaxation Times Maps Reconstruction and Unsupervised Classification in Magnitude Magnetic Resonance Imaging

“…A step of data classification in the space formed by the estimated parameters is suggested in order to extract a distribution of the estimated T 2 parameters at different spatial regions of the image. In this paper, an efficient penalized ML algorithm is presented in order to carry out the estimation on the whole image at once and obtain voxel level information [2]. The first feature of the algorithm is to estimate all the image parameters simultaneously using a Majorization-Minimization (MM) approach leading to a quadratic majorant function to be minimized with an adapted Levenberg-Marquardt (LM) algorithm.…”