Data inversion of multi-dimensional magnetic resonance in porous media

Since its inception in the 1970s, multi-dimensional magnetic resonance (MR) has emerged as a powerful tool for non-invasive investigations of structures and molecular interactions. MR spectroscopy beyond one dimension allows the study of the correlation, exchange processes, and separation of overlapping spectral information. The multi-dimensional concept has been re-implemented over the last two decades to explore molecular motion and spin dynamics in porous media. Apart from Fourier transform, methods have been developed for processing the multi-dimensional time-domain data, identifying the fluid components, and estimating pore surface permeability via joint relaxation and diffusion spectra. Through the resolution of spectroscopic signals with spatial encoding gradients, multi-dimensional MR imaging has been widely used to investigate the microscopic environment of living tissues and distinguish diseases. Signals in each voxel are usually expressed as multi-exponential decay, representing microstructures or environments along multiple pore scales. The separation of contributions from different environments is a common ill-posed problem, which can be resolved numerically. Moreover, the inversion methods and experimental parameters determine the resolution of multi-dimensional spectra. This paper reviews the algorithms that have been proposed to process multi-dimensional MR datasets in different scenarios. Detailed information at the microscopic level, such as tissue components, fluid types and food structures in multi-disciplinary sciences, could be revealed through multi-dimensional MR.