Author: Oluyemi Bright Aboyewa, KyungPyo Hong, Daniel Kim 👨🔬
Affiliation: Department of Radiology, Northwestern University 🌍
Purpose: While non-Cartesian MRI is desirable for fast imaging with high spatial resolution and robustness to motion, it requires long post-processing times. Preconditioning with an adequate density compensation function (DCF) may accelerate the convergence of iterative image reconstruction methods (e.g., compressed sensing). We sought to extend the concept of the geometrically-derived DCF (gDCF), previously validated for 2D radial MRI, to 3D non-Cartesian trajectory MRI.
Methods: In gDCF, a sample weight is calculated as the inverse sum of the degree of overlap at the sample location in k-space with other samples within a distance approximated by the Nyquist distance (∆k=1/Field-of-View). Our experiments utilized numerical simulations and a publicly available T1-weighted 3D brain MRI dataset (reference). We compared the performance of gDCF to rho-filter (standard; radial only) and Pipe-DCF in gridding reconstruction using fully-sampled 3D radial (spiral-phyllotaxis scheme) and cone trajectory k-space datasets. We then evaluated their performance in initial preconditioning prior to iterative reconstruction using 25-fold undersampled radial and cone trajectory k-space datasets. Image quality was quantified by root-mean-square error (RMSE), structural similarity index (SSIM), and the peak signal-to-noise ratio (PSNR) compared to the reference.
Results: For the fully-sampled datasets, Rho-filter showed the best metric of RMSE=0.014, SSIM=0.98, and PSNR=36.82 in 3D radial, while gDCF (RMSE=0.04 & 0.065; SSIM=0.93 & 0.91; PSNR=27.99 & 23.76) performed better than Pipe-DCF (RMSE=0.13 & 0.12; SSIM=0.81 & 0.83; PSNR=18.07 & 18.65) in both 3D radial and cone dataset, respectively. For undersampled 3D radial and cone datasets, gDCF (RMSE=0.051 & 0.085; SSIM=0.88 & 0.82, PSNR=25.82 & 21.42) outperformed both Pipe-DCF (RMSE=0.14 & 0.12; SSIM=0.79 & 0.81, PSNR=17.38 & 18.37) and Rho-filter (RMSE=0.16; SSIM=0.75, PSNR=15.89).
Conclusion: This numerical simulation study demonstrated that gDCF provided improved image quality for initial preconditioning of iterative reconstruction in 25-fold accelerated 3D MRI using radial and cone k-space sampling trajectories.