Abstract
Combined relaxation-diffusion MRI (rdMRI) is a technique to probe tissue microstructure using diffusion MRI data with multiple b-values and echo time. Joint analysis of rdMRI data can characterize the joint relaxation and diffusion distribution (RDD) function to examine heterogeneous tissue microstructure without using multi-component models. This paper shows that the problem of estimating RDD functions is equivalent to the multivariate Hausdorff moment problem by applying a change of variables. Three formulations of maximum entropy (ME) estimation problems are proposed to solve the inverse problem to derive ME-RDD functions in different parameter spaces. All three formulations can be solved by using convex optimization algorithms. The performance of the proposed algorithms is compared with the standard methods using basis functions based on simulations and in vivo rdMRI data. Results show that the proposed methods provide a more accurate estimation of RDD functions than basis-function methods.
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Ning, L. (2023). Maximum-Entropy Estimation of Joint Relaxation-Diffusion Distribution Using Multi-TE Diffusion MRI. In: Greenspan, H., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2023. MICCAI 2023. Lecture Notes in Computer Science, vol 14227. Springer, Cham. https://doi.org/10.1007/978-3-031-43993-3_43
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