Cumulant expansion with localization: A new representation of the diffusion MRI signal

Diffusion MR is sensitive to the microstructural features of a sample. Fine-scale characteristics can be probed by employing strong diffusion gradients while the low b-value regime is determined by the cumulants of the distribution of particle displacements. A signal representation based on the cumulants, however, suffers from a finite convergence radius and cannot represent the 'localization regime' characterized by a stretched exponential decay that emerges at large gradient strengths. Here, we propose a new representation for the diffusion MR signal. Our method provides not only a robust estimate of the first three cumulants but also a meaningful extrapolation of the entire signal decay.