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.
In clinical and biological applications of T2 relaxometry, a multi-exponential decay model proved to be representative of the relaxation signal inside each voxel of the MRI images. However, estimating and exploiting the model parameters for magnitude data is a large-scale ill-posed inverse problem. This paper presents a parameter estimation method that combines a spatial regularization with a Maximum-Likelihood criterion based on the Rician distribution of the noise. In order to properly carry out the estimation on the image level, a Majorization-Minimization approach is implemented alongside an adapted non-linear least-squares algorithm. We propose a method for exploiting the reconstructed maps by clustering the parameters using a K-means classification algorithm applied to the extracted relaxation time and amplitude maps. The method is illustrated on real MRI data of food sample analysis.
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