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

• Published in: Magnetic resonance in medicine Vol. 82; no. 3; pp. 1101 - 1112
• Main Authors: Luo, Tianrui, Noll, Douglas C., Fessler, Jeffrey A., Nielsen, Jon‐Fredrik
• Format: Journal Article
• Language: English
• Published: United States Wiley Subscription Services, Inc 01.09.2019
• Subjects: Algorithms; Boundary conditions; Calibration; Cartesian coordinates; Computers; Constellations; Datasets; dynamic imaging; Error detection; Fourier transforms; Functional magnetic resonance imaging; GRAPPA; g‐factor; Image quality; Image reconstruction; In vivo methods and tests; Kernels; Motor task performance; non‐cartesian imaging; non‐iterative reconstruction; NUFFT; Phase transitions; Sampling; Spirals; Trajectories; g-factor; GRAPPA; non-iterative reconstruction; non-cartesian imaging; NUFFT; dynamic imaging
• ISSN: 0740-3194; 1522-2594; 1522-2594
• DOI: 10.1002/mrm.27801

Purpose GRAPPA is a popular reconstruction method for Cartesian parallel imaging, but is not easily extended to non‐Cartesian sampling. We introduce a general and practical GRAPPA algorithm for arbitrary non‐Cartesian imaging. Methods We formulate a general GRAPPA reconstruction by associating a unique kernel with each unsampled k‐space location with a distinct constellation, that is, local sampling pattern. We calibrate these generalized kernels using the Fourier transform phase shift property applied to fully gridded or separately acquired Cartesian Autocalibration signal (ACS) data. To handle the resulting large number of different kernels, we introduce a fast calibration algorithm based on nonuniform FFT (NUFFT) and adoption of circulant ACS boundary conditions. We applied our method to retrospectively under‐sampled rotated stack‐of‐stars/spirals in vivo datasets, and to a prospectively under‐sampled rotated stack‐of‐spirals functional MRI acquisition with a finger‐tapping task. Results We reconstructed all datasets without performing any trajectory‐specific manual adaptation of the method. For the retrospectively under‐sampled experiments, our method achieved image quality (i.e., error and g‐factor maps) comparable to conjugate gradient SENSE (cg‐SENSE) and SPIRiT. Functional activation maps obtained from our method were in good agreement with those obtained using cg‐SENSE, but required a shorter total reconstruction time (for the whole time‐series): 3 minutes (proposed) vs 15 minutes (cg‐SENSE). Conclusions This paper introduces a general 3D non‐Cartesian GRAPPA that is fast enough for practical use on today’s computers. It is a direct generalization of original GRAPPA to non‐Cartesian scenarios. The method should be particularly useful in dynamic imaging where a large number of frames are reconstructed from a single set of ACS data.