Multi-Exponential Transverse Relaxation Times Estimation From Magnetic Resonance Images Under Rician Noise and Spatial Regularization

Abstract

Relaxation signal inside each voxel of magnetic resonance images (MRI) is commonly fitted by a multi-exponential decay curve. The estimation of a discrete multi-component relaxation model parameters from magnitude MRI data is a challenging nonlinear inverse problem since it should be conducted on the entire image voxels under non-Gaussian noise statistics. This paper proposes an efficient algorithm allowing the joint estimation of relaxation time values and their amplitudes using different criteria taking into account a Rician noise model, combined with a spatial regularization accounting for low spatial variability of relaxation time constants and amplitudes between neighboring voxels. The Rician noise hypothesis is accounted for either by an adapted nonlinear least squares algorithm applied to a corrected least squares criterion or by a majorizationminimization approach applied to the maximum likelihood criterion. In order to solve the resulting large-scale non-negativity constrained optimization problem with a reduced numerical complexity and computing time, an optimization algorithm based on a majorization approach ensuring separability of variables between voxels is proposed. The minimization is carried out iteratively using an adapted Levenberg-Marquardt algorithm that ensures convergence by imposing a sufficient decrease of the objective function and the non-negativity of the parameters. The importance of the regularization alongside the Rician noise incorporation is shown both visually and numerically on a simulated phantom and on magnitude MRI images acquired on fruit samples.

Quantitative MRI analysis of structural changes in tomato tissues resulting from dehydration

“…Multi‐exponential T 2 maps of the tomato slices before and after dehydration were calculated using the algorithm implemented in MATLAB software described in El‐Hajj et al, [ 30 ] based on a discrete model with a priori known number of components. The method is iterative and based on the maximization of the likelihood criterion under the hypothesis of Rician noise, with spatial regularity imposed to achieve noise reduction.…”

“…[32] Following dehydration, the apparent microporosity maps contained magnetic susceptibility artifacts and could therefore not be used. The method described in El-Hajj et al [30] allowed multi-T 2 relaxation parameter maps to be estimated, making it possible to access information on different water pools in each voxel. This approach has made possible interesting observations that could not be carried out using mono-exponential relaxation maps.…”

“…This work therefore aims to study the variations in transverse relaxation signal during the dehydration process in tomato, considering both the effect of the water content and structural variations within the tissues. An MRI approach was employed [10,30] for the estimation of the multi-T 2 relaxation parameters at the voxel scale. The study was performed on tomato, which offers a welldocumented model where the tissues have different intrinsic microstructures in terms of cell size [31] and gas proportion, [32] thereby providing an ideal subject for the purpose of the present study.…”

Model-Informed Machine Learning for Multi-component T2 Relaxometry

“…Our method, as well as the other methods compared to in this work, reconstruct the T 2 distribution in each voxel separately. However, there are parametric and non-parametric approaches to T 2 relaxometry which use spatial regularization (El-Hajj et al, 2020;Hwang and Du, 2009;Kumar et al, 2018). These approaches assume that voxels spatially close to each other should also have similar reconstructions; hence, they perform reconstructions on groups of adjacent voxels simultaneously, with constraints that limit the variation of the reconstructions over the group.…”

Relaxation spectral analysis in multi‐contrast vascular magnetic particle imaging

“…11 The recovery of magnetization in the field-flat phase can be described using a multi-exponential recovery model. 20 The relaxation spectrum 21 can be generated using the inverse Laplace transform (ILT) to accurately measure the Néel and Brownian relaxation components.…”