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Updated: May 14, 2026
Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
Published on: July 28, 2013
Geometrically-derived density compensation function for gridding reconstruction of 2D and 3D non-Cartesian MRI data
Oluyemi Aboyewa1, Daniel Kim1, KyungPyo Hong2
1Department of Biomedical Engineering, Northwestern University, Evanston, IL, United States of America; Department of Radiology, Feinberg School of Medicine, Northwestern University, Chicago, IL, United States of America.
Purpose:
Density compensation function (DCF) is essential for minimizing reconstruction errors in non-Cartesian MRI. This study aimed to extend a geometrically-derived DCF (gDCF), previously validated for 2D radial MRI, to arbitrary 2D and 3D non-Cartesian k-space sampling trajectories.
Methods:
In the gDCF framework, sample weights were analytically computed as the inverse sum of the overlap degrees between neighboring radial k-space samples, using a Nyquist sampling distance, ∆k. To generalize gDCF beyond radial trajectories, a direction-independent ∆k was introduced. Three approaches for redefining the sampling distance were evaluated: Nyquist distance (∆kNyq=1/Field-of-View), generalized FOV (∆kgen), and Beruling-Landau density condition (∆kBL). To account for modulation introduced by the convolution kernel used in the gridding reconstruction, a kernel correction was integrated into the gDCF formulation. The proposed gDCF methods were evaluated using numerical simulations on fully sampled 2D phantom and T1-weighted 3D brain MRI datasets. Performance was benchmarked against existing DCF methods, including ramp/rho-filter, Voronoi, Pipe, and LSQR, using radial, spiral, rosette, and cone k-space trajectories. Image quality was quantitatively assessed using root-mean-square error (RMSE) and structural-similarity index (SSIM) against the fully sampled references.
Results:
In 2D simulations, kernel-corrected gDCF achieved reconstruction accuracy (RMSE≤0.0190 and SSIM≥0.9756) comparable to Pipe (RMSE≤0.0189; SSIM≥0.9758) across all trajectories. In 3D simulations, kernel-corrected gDCFNyq outperformed the Rho-filter but remained less accurate than Pipe. Nevertheless, gDCFNyqwas ∼2× faster than Pipe at larger k-space matrix sizes.
Conclusions:
This study demonstrated that gDCF could be extended to arbitrary non-Cartesian trajectories, providing accurate and computationally efficient density compensations for gridding-based MRI reconstruction.
