On NUFFT-based gridding for non-Cartesian MRI

Abstract

For MRI with non-Cartesian sampling, the conventional approach to reconstructing images is to use the gridding method with a Kaiser-Bessel (KB) interpolation kernel. Recently, Sha et al. [1] proposed an alternative method based on a nonuniform FFT (NUFFT) with least-squares (LS) design of the interpolation coefficients. They described this LS_NUFFT method as shift variant and reported that it yielded smaller reconstruction approximation errors than the conventional shift-invariant KB approach. This paper analyzes the LS_NUFFT approach in detail. We show that when one accounts for a certain linear phase factor, the core of the LS_NUFFT interpolator is in fact real and shift invariant. Furthermore, we find that the KB approach yields smaller errors than the original LS_NUFFT approach. We show that optimizing certain scaling factors can lead to a somewhat improved LS_NUFFT approach, but the high computation cost seems to outweigh the modest reduction in reconstruction error. We conclude that the standard KB approach, with appropriate parameters as described in the literature, remains the practical method of choice for gridding reconstruction in MRI.

MR fingerprinting for rapid quantification of myocardial T1 , T2 , and proton spin density

“…Data are sampled along a variable density spiral having a minimum time gradient design (32), which requires 24 interleaves to fully sample the center 25% of k-space and 48 interleaves to completely satisfy the Nyquist criterion at the edges of a 192x192 k-space matrix. A time series of undersampled (acceleration factor R=48) images is generated by gridding each single-shot interleaf using the NUFFT (33). Individually, each image is degraded by severe aliasing artifacts.…”

Modified Wavenumber Domain Algorithm for Three-Dimensional Millimeter-Wave Imaging

“…The cubic target model consisting of 8 scatterers. Figure 3 shows the phase of the signal after matched filtering with a reference function that makes the stop-and-go approximation, i.e., the phase of the remaining signal after (14) is multiplied by (24). The phase of the remaining signal in the elevation-frequency and range-frequency domain, i.e., in the k y − k r domain, is shown in Figure 3(a), and the phase in the elevation-frequency and azimuthfrequency domain, i.e., in the k y − k x domain, is illustrated in Figure 3(b).…”

“…The NUFFT approaches have been developed to overcome the limitation of equally spaced sampling needed by FFT [17][18][19][20][21][22][23]. NUFFTs have wide applications in magnetic resonance image reconstruction [24], ground penetrating radar with the range migration algorithm [16], synthetic aperture imaging radiometers [25], and near-field imaging [26]. In this paper, the 3-D NUFFT is used to replace the Stolt interpolation and the followed 3-D IFFT to improve the computational efficiency.…”

Dictionary Learning and Time Sparsity for Dynamic MR Data Reconstruction

“…We only consider the case of Cartesian undersampling, which is the most common in practice, although more elaborate sampling strategies like radial or spiral [45], [46] could be equally possible with modifications on the data consistency step and using non-uniform Fourier transforms [47]. Even though greater aliasing incoherence can be achieved with 2D k-space undersampling [45], frequency encodes can be considered instantaneous relative to phase encodes, so acceleration is only meaningful through phase encode undersampling.…”