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

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 multi-exponential 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.