title: A rapid look-up table method for reconstructing MR images from arbitrary K-space trajectories.
abstract: Look-up tables (LUTs) are a common method for increasing the speed of many algorithms. Their use can be extended to the reconstruction of nonuniformly sampled k-space data using either a discrete Fourier transform (DFT) algorithm or a convolution-based gridding algorithm. A table for the DFT would be precalculated arrays of weights describing how each data point affects all of image space. A table for a convolution-based gridding operation would be a precalculated table of weights describing how each data point affects a small k-space neighborhood. These LUT methods were implemented in C++ on a modest personal computer system; they allowed a radial k-space acquisition sequence, consisting of 180 views of 256 points each, to be gridded in 36.2 ms, or, in approximately 800 ns/point. By comparison, a similar implementation of the gridding operation, without LUTs, required 45 times longer (1639.2 ms) to grid the same data. This was possible even while using a 4 x 4 Kaiser-Bessel convolution kernel, which is larger than typically used. These table-based computations will allow real time reconstruction in the future and can currently be run concurrently with the acquisition allowing for completely real-time gridding.
authors.affiliation: Department of Radiology and Biomedical Engineering, Case Western Reserve University and University Hospitals of Cleveland, OH 44106, USA.
authors.forename: B
authors.initials: B
authors.lastname: Dale
authors.forename: M
authors.initials: M
authors.lastname: Wendt
authors.forename: J L
authors.initials: JL
authors.lastname: Duerk
mesh_terms: D000465:Algorithms; D000818:Animals; D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008962:Models, Theoretical; D013552:Swine