Improved data efficiency for NMR diffusion-relaxation processing

Two dimensional diffusion and transverse (T₂) NMR relaxation measurements are effective for a variety of research and industrial processes. Conversion of the measurements into a D-T₂ map is performed using an inverse integral transformation. A difficulty with D-T₂ estimation from data acquired without pulsed field gradients (using, for example, the inherent static field gradient of a single-sided magnet) is that the diffusion and relaxation kernels are coupled. One commonly used solution is to introduce a time offset to enable the kernels to be decoupled, but this has the undesirable results of causing some of the data, and a large proportion of the signal energy, to become unusable. This paper presents two methods of processing the data that do not require this wastage. Both methods are based on insights that arise from considering the linear operator that describes the forwards integral transformation. One method involves data compression, while the other method is an application (that we call FLINT) of the fast iterative soft thresholding algorithm. Both methods are able to use all of the available data. The paper demonstrates the improved accuracy that results from these methods on simulated data, as well as the improved discovery of important features on measured data.