Acquisition of spatially-resolved displacement propagators using compressed sensing APGSTE-RARE MRI

A method is presented for accelerating the acquisition of spatially-resolved displacement propagators via under-sampling of an Alternating Pulsed Gradient Stimulated Echo - Rapid Acquisition with Relaxation Enhancement (APGSTE-RARE) data acquisition with compressed sensing image reconstruction. The method was demonstrated with respect to the acquisition of 2D spatially-resolved displacement propagators of water flowing through a packed bed of hollow cylinders. The q,k-space was under-sampled according to variable-density pseudo-random sampling patterns. The quality of compressed sensing reconstructions of spatially-resolved propagators at a range of sampling fractions was assessed using the peak signal-to-noise ratio (PSNR) as a quality metric. Propagators of good quality (PSNR 33.2 dB) were reconstructed from only 6.25% of all data points in q,k-space, resulting in a reduction in the data acquisition time from 4 h to 14 min. The spatially-resolved propagators were reconstructed using both the total variation and nuclear norm sparsifying transforms; use of total variation resulted in a slightly higher quality of the reconstructed image in most cases. To illustrate the power of this method to characterise heterogeneous flow in porous media, the method is applied to the characterisation of flow in a vuggy carbonate rock.