A rapid look-up table method for reconstructing MR images from arbitrary K-space trajectories

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) algor ithm or a convolution-based gridding algorithm. A table for the DFT would b e precalculated arrays of weights describing how each data point affects al l 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 Ic-space acquisiti on sequence, consisting of 180 views of 256 points each, to be gridded in 3 6.2 ms, or, in approximately 800 ns/point, By comparison, a similar impleme ntation 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. Th ese table-based computations will allow real time reconstruction in the fut ure and can currently be run concurrently with the acquisition allowing for completely real-time gridding.