CT image reconstruction using hexagonal grids

Michael Knaup, Sven Steckmann, Olivier Bockenbach, and Marc Kachelriess
Institute of Medical Physics (IMP), University of Erlangen-Nurnberg, Germany
IEEE Nuclear Science Symposium Conference Record, 2007. NSS ’07


   title={CT image reconstruction using hexagonal grids},

   author={Knaup, M. and Steckmann, S. and Bockenbach, O. and Kachelrie{ss}, M.},

   booktitle={Nuclear Science Symposium Conference Record, 2007. NSS’07. IEEE},






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In the transversal plane CT exhibits a nearly rotational symmetric point spread function. Pixel sampling is typically done on Cartesian grids which are not ideal from a signal processing point of view. It is advantageous to use a hexagonal grid which can capture the same signal components with 13% fewer sampling points. In 3D one can even save 29%. We developed an efficient scheme to allow for arbitrarily shaped field of views and a hierarchical memory layout. The latter divides the images into small hexagonal subimages, similar to honeycombs, whose size is small enough to avoid cache misses on CPU-based algorithms or to be used on dedicated signal processing hardware such as GPUs (graphics processing units) or CBEs (cell broadband engines) that may be memory limited. As the final step a resampling algorithm converts from the hex domain to the Cartesian domain before storing images. We implemented a hyperfast CBE-based Feldkamp algorithm for the hexagonal lattice and compared its performance and its image quality to reconstructions using the standard Feldkamp algorithm. Both algorithms were run on the Dual Cell Based System (DCBS, Mercury Computer Systems, Berlin, Germany) on two CBEs with 3.2 GHz each. A 5123 volume was reconstructed from 720 projections of 5122 detector pixels. Image quality of the hexagonal approach was identical to the direct approach using the Cartesian lattice: the maximum relative difference between the MTFs was 1% and image noise differed by not more than 3%. The improvement in reconstruction speed was approximately 12% for the hexagonal grid which is slightly lower than the expectation. The complete reconstruction finished in about 10 s. With identical image quality reconstruction on the hexagonal grid is a simple and effective approach to significantly reduce memory consumption and reconstruction time. Existing reconstruction algorithms can be easily modified to operate in the hexagonal domain.
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