A fast implementation of the incremental backprojection algorithms for parallel beam geometries
- National Taiwan Univ., Taipei (Taiwan, Province of China). Center for Biomedical Engineering
- Univ. of California, Irvine, CA (United States). Dept. of Radiological Sciences
Filtered-backprojection algorithms are the most widely used approaches for reconstruction of computed tomographic (CT) images, such as X-ray CT and positron emission tomographic (PET) images. The Incremental backprojection algorithm is a fast backprojection approach based on restructuring the Shepp and Logan algorithm. By exploiting interdependency (position and values) of adjacent pixels, the Incremental algorithm requires only O(N) and O(N{sup 2}) multiplications in contrast to O(N{sup 2}) and O(N{sup 3}) multiplications for the Shepp and Logan algorithm in two-dimensional (2-D) and three-dimensional (3-D) backprojections, respectively, for each view, where N is the size of the image in each dimension. In addition, it may reduce the number of additions for each pixel computation. The improvement achieved by the Incremental algorithm in practice was not, however, as significant as expected. One of the main reasons is due to inevitably visiting pixels outside the beam in the searching flow scheme originally developed for the Incremental algorithm. To optimize implementation of the Incremental algorithm, an efficient scheme, namely, coded searching flow scheme, is proposed in this paper to minimize the overhead caused by searching for all pixels in a beam. The key idea of this scheme is to encode the searching flow for all pixels inside each beam. While backprojecting, all pixels may be visited without any overhead due to using the coded searching flow as the a priori information. The proposed coded searching flow scheme has been implemented on a Sun Sparc 10 and a Sun Sparc 20 workstations. The implementation results show that the proposed scheme is 1.45--2.0 times faster than the original searching flow scheme for most cases tested.
- Sponsoring Organization:
- National Science Council, Taipei (Taiwan, Province of China)
- OSTI ID:
- 458241
- Report Number(s):
- CONF-951073-; ISSN 0018-9499; TRN: 97:006824
- Journal Information:
- IEEE Transactions on Nuclear Science, Vol. 43, Issue 6Pt2; Conference: IEEE nuclear science symposium and medical imaging conference, San Francisco, CA (United States), 21-28 Oct 1995; Other Information: PBD: Dec 1996
- Country of Publication:
- United States
- Language:
- English
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