Fully three-dimensional reconstruction from data collected on concentric cubes in Fourier space: implementation and a sample application to MRI [magnetic resonance imaging]

An algorithm is proposed for rapid and accurate reconstruction from data collected in Fourier space at points arranged on a grid of concentric cubes. The whole process has computational complexity of the same order as required for the 3D fast Fourier transform and so (for medically relevant sizes of the data set) it is faster than backprojection into the same size rectangular grid. The design of the algorithm ensures that no interpolations are needed, in contrast to methods involving backprojection with their unavoidable interpolations. As an application, a 3D data collection method for MRI has been designed which directly samples the Fourier transform of the object to be reconstructed on concentric cubes as needed for the algorithm. (author)