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

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.