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An improved gridding method for spiral MRI using nonuniform fast Fourier transform
Liewei Sha1, Hua Guo, Allen W Song
1Department of Electrical and Computer Engineering, Duke University, USA.
Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|June 18, 2003
Summary
A new gridding method, LS-NUFFT, enhances spiral MRI image reconstruction by minimizing errors. This method offers improved accuracy over Kaiser-Bessel gridding with similar computational demands.
Area of Science:
- Medical Imaging
- Signal Processing
- Computational Science
Background:
- Nonuniform Fast Fourier Transform (NUFFT) algorithms are crucial for image reconstruction in Magnetic Resonance Imaging (MRI).
- Spiral MRI trajectories present unique challenges for standard gridding methods due to their nonuniform k-space sampling.
- Existing methods like Kaiser-Bessel gridding and generalized FFT (GFFT) have limitations in minimizing reconstruction errors for these trajectories.
Purpose of the Study:
- To extend the Liu and Nguyen algorithm for nonuniform fast Fourier transform (NUFFT) to two dimensions for spiral MRI image reconstruction.
- To introduce and evaluate a novel gridding method, LS-NUFFT (Least Square NUFFT), designed to minimize reconstruction approximation error.
- To analytically and experimentally compare LS-NUFFT with conventional gridding techniques.
Main Methods:
- The LS-NUFFT method was developed by generating convolution kernels optimized for spiral k-space trajectories, minimizing error in the Least Square sense.
- Analytical comparisons were performed within a framework including Kaiser-Bessel gridding and a generalized FFT (GFFT) approach.
- Experimental validation involved assessing LS-NUFFT performance against direct summation and Kaiser-Bessel gridding using digital phantoms and in vivo MRI data.
Main Results:
- LS-NUFFT demonstrated a smaller reconstruction approximation error compared to the standard Kaiser-Bessel gridding method.
- The computational complexity of LS-NUFFT was found to be equivalent to that of the Kaiser-Bessel gridding method.
- Reconstruction results using both phantom and in vivo data confirmed the superior accuracy of LS-NUFFT.
Conclusions:
- LS-NUFFT provides a more accurate image reconstruction for spiral MRI compared to existing methods like Kaiser-Bessel gridding.
- The method achieves improved accuracy without increasing computational cost, making it an efficient alternative.
- LS-NUFFT represents a significant advancement in MRI image reconstruction, particularly for nonuniform sampling trajectories.