Technical Note: Evaluation of pre‐reconstruction interpolation methods for iterative reconstruction of radial k‐space data

Abstract

Purpose To evaluate the use of three different pre-reconstruction interpolation methods to convert non-Cartesian k-space data to Cartesian samples such that iterative reconstructions can be performed more simply and more rapidly. Methods Phantom as well as cardiac perfusion radial datasets were reconstructed by four different methods. Three of the methods used pre-reconstruction interpolation once followed by a fast Fourier transform (FFT) at each iteration. The methods were: bilinear interpolation of nearest-neighbor points (BINN), 3-point interpolation, and a multi-coil interpolator called GRAPPA Operator Gridding (GROG). The fourth method performed a full non-Uniform FFT (NUFFT) at each iteration. An iterative reconstruction with spatiotemporal total variation constraints was used with each method. Differences in the images were quantified and compared. Results The GROG multi-coil interpolation, the 3-point interpolation, and the NUFFT-at-each-iteration approaches produced high quality images compared to BINN, with the GROG-derived images having the fewest streaks among the three pre-interpolation approaches. However, all reconstruction methods produced approximately equal results when applied to perfusion quantitation tasks. Pre-reconstruction interpolation gave approximately an 83% reduction in reconstruction time. Conclusion Image quality suffers little from using a pre-reconstruction interpolation approach compared to the more accurate NUFFT-based approach. GROG-based pre-reconstruction interpolation appears to offer the best compromise by using multi-coil information to perform the interpolation to Cartesian sample points prior to image reconstruction. Speed gains depend on the implementation and relatively standard optimizations on a MATLAB platform result in pre-interpolation speedups of ~6 compared to using NUFFT at every iteration, reducing the reconstruction time from around 42 minutes to 7 minutes.

Quantitative 3D myocardial perfusion with an efficient arterial input function

“…Images were reconstructed using a joint multi‐coil temporally and spatially constrained reconstruction technique. Both 2D and 3D datasets were preinterpolated with GRAPPA operating gridding (GROG) . The GROG operator was computed on a slice by slice basis.…”

RACER‐GRASP: Respiratory‐weighted, aortic contrast enhancement‐guided and coil‐unstreaking golden‐angle radial sparse MRI

“…The phase at − 30 s is selected as the precontrast phase; the phases at + 5, + 10, and +15 s are selected as the early to late arterial phases; the phase at + 60 s is selected as the portal venous phase; and the phase at +180 s is selected as the equilibrium phase. Note that in clinical workflow, all phases can be automatically exported for a radiologist based on their time stamps without user interaction. Each contrast phase is binned into multiple motion phases spanning from end‐expiration to end‐inspiration using the extracted respiratory motion signal, as shown in Supporting Figure S3 as an example of four respiratory phases. Multicoil radial k‐space data in each sorted dynamic phase are gridded onto a Cartesian grid using self‐calibrating GRAPPA operator gridding (GROG) (Eq. ), such that the subsequent iterative reconstruction can be performed directly on the Cartesian space.…”

“…Multicoil radial k‐space data in each sorted dynamic phase are gridded onto a Cartesian grid using self‐calibrating GRAPPA operator gridding (GROG) (Eq. ), such that the subsequent iterative reconstruction can be performed directly on the Cartesian space.…”

A GRAPPA algorithm for arbitrary 2D/3D non‐Cartesian sampling trajectories with rapid calibration

“…We propose a conceptually simple method for generalizing GRAPPA to arbitrary 3D non‐Cartesian PI acquisitions, and provide an efficient algorithm for its calibration . For each unsampled k‐space location (with a distinct local sampling constellation), our method assigns a unique GRAPPA kernel, whose calibration is efficiently implemented by utilizing the phase‐shift property of the Fourier Transform (FT) and the NUFFT . Like Cartesian GRAPPA, our method does not require explicit coil sensitivity information, and reconstruction per image volume (once weights have been calibrated) is rapid.…”