Fast direct Fourier methods, based on one- and two-pass coordinate transformations, yield accurate reconstructions of x-ray CT clinical images

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Abstract
The conversion from polar to Cartesian coordinates can be carried out with two-pass algorithms. The paper describes two different methods based on concentric square frames and octagonal frames and their results, obtained with accurate interpolations based on the `moving window Shannon reconstruction' (MWSR). The embedding of these algorithms in direct Fourier methods (DFMs) of tomographic reconstruction is discussed. With respect to one-pass methods and to the use of octagonal frames, the square frame method makes it possible to carry out the first pass, a radial resampling, in the direct space, before computing 1D Fourier transforms (FTs) of projections. Reconstructions of clinical images from the raw data of a third-generation x-ray tomograph are presented and compared with those obtained with one-pass DFMs and with the convolution back-projection method (CBPM) performed by the instrument. The simple algorithm using square frames yields results in complete agreement with other DFM protocols and the CBPM. On a general-purpose computer, the execution of DFM protocols based on one-pass and two-pass coordinate transformations is 35 to 55 times faster than the CBPM and make the algorithms attractive for modern instrumentation.

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