Accelerating compressed sensing reconstruction of subsampled radial k-space data using geometrically-derived density compensation

Objective. To accelerate compressed sensing (CS) reconstruction of subsampled radial k-space data using a geometrically-derived density compensation function (gDCF) without significant loss in image quality. Approach. We developed a theoretical framework to calculate a gDCF based on Nyquist distance along the radial and circumferential directions of a discrete polar coordinate system. Our gDCF was compared against standard DCF (e.g. ramp filter) and another commonly used DCF (modified Shepp-Logan (SL) filter). The resulting image quality produced by each DCF was quantified using normalized root-mean-square-error (NRMSE), blur metric (1 = blurriest; 0 = sharpest), and structural similarity index (SSIM; 1 = perfect match; 0 = no match) compared with the reference. For filtered backprojection (FBP) of phantom data obtained at the Nyquist sampling rate, Cartesian k-space sampling was used as the reference. For CS reconstruction of subsampled cardiac magnetic resonance imaging datasets (real-time cardiac cine data with 11 projections per frame, n = 20 patients; cardiac perfusion data with 30 projections per frame, n = 19 patients), CS reconstruction without DCF was used as the reference. Main results. The NRMSE, SSIM, and blur metrics of the phantom data were good for all DCFs, confirming that our gDCF produces uniform densities at the upper limit (Nyquist). For CS reconstruction of subsampled real-time cine and cardiac perfusion datasets, the image quality metrics (SSIM, NRMSE) were significantly (p < 0.05) higher for our gDCF than other DCFs, and the reconstruction time was significantly (p < 0.05) faster for our gDCF (reference) than no DCF (11.9%-52.9% slower), standard DCF (23.9%-57.6% slower), and modified SL filter (13.5%-34.8% slower). Significance. The proposed gDCF accelerates CS reconstruction of subsampled radial k-space data without significant loss in image quality compared with no DCF as the reference.

Automated summary

The study developed a method to accelerate compressed sensing reconstruction of subsampled radial k-space data without significant loss in image quality. Comparison showed that the method outperformed other techniques in reconstructing subsampled real-time cine and cardiac perfusion datasets.