On uniqueness of coefficient identification in the Bloch–Torrey equation for magnetic resonance imaging
Abstract
In this paper, we provide some uniqueness results for the (multi-)coefficient identification problem of reconstructing the spatially varying spin density as well as the spin–lattice and spin–spin relaxation times and the local field inhomogeneity in the Bloch–Torrey equation, as relevant in magnetic resonance imaging MRI. To this end, we follow two approaches: (a) Relying on sampling of the k-space and (approximately) explicit reconstruction formulas in the simplified (Bloch) ODE setting, along with perturbation estimates; (b) Relying on infinite speed of propagation due to diffusion. The results on well-posedness and Lipschitz continuous differentiability of the coefficient-to-state map derived for this purpose, are expected to be useful also in the convergence analysis of reconstruction schemes as well in mathematical optimization of the experimental design in MRI.
Fields of Study & Subjects
Numerical methods in inverse problems
Medical Imaging Techniques and Applications
Advanced MRI Techniques and Applications
Publication details
- Journal / source
- Mathematical Models and Methods in Applied Sciences
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 36
- Issue
- 11
- Pages
- 2517–2560
- Publication date
- 8 May 2026
- Language
- EN