### Abstract

We introduce a fast algorithm for backprojecting images from tomographic fan-beam projections that aggregates the projections in a hierarchical structure and achieves a computational cost of O(N ^{2} log P), when backprojecting an N × N pixel image from P projections. Like in the parallel-beam algorithm in [1], the images in the hierarchy are formed by the rotation and the adding together of other images made up of fewer projections. The low computational cost of the algorithm depends on the efficient sampling of the intermediate images in the hierarchy. Understanding the algorithm within the signal processing framework, a general scheme for sampling an image made up of projections of arbitrary geometries is introduced. While the algorithm is related to one by Nilsson [2], the Fourier domain understanding leads to a more efficient sampling scheme for the intermediate images.

Original language | English (US) |
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Title of host publication | 2006 3rd IEEE International Symposium on Biomedical Imaging |

Subtitle of host publication | From Nano to Macro - Proceedings |

Pages | 1188-1191 |

Number of pages | 4 |

State | Published - Nov 17 2006 |

Event | 2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Arlington, VA, United States Duration: Apr 6 2006 → Apr 9 2006 |

### Publication series

Name | 2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings |
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Volume | 2006 |

### Other

Other | 2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro |
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Country | United States |

City | Arlington, VA |

Period | 4/6/06 → 4/9/06 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings*(pp. 1188-1191). [1625136] (2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings; Vol. 2006).

**A fast and accurate decimation-in-angle hierarchical fan-beam backprojection algorithm.** / George, Ashvin; Bresler, Yoram.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings.*, 1625136, 2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings, vol. 2006, pp. 1188-1191, 2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Arlington, VA, United States, 4/6/06.

}

TY - GEN

T1 - A fast and accurate decimation-in-angle hierarchical fan-beam backprojection algorithm

AU - George, Ashvin

AU - Bresler, Yoram

PY - 2006/11/17

Y1 - 2006/11/17

N2 - We introduce a fast algorithm for backprojecting images from tomographic fan-beam projections that aggregates the projections in a hierarchical structure and achieves a computational cost of O(N 2 log P), when backprojecting an N × N pixel image from P projections. Like in the parallel-beam algorithm in [1], the images in the hierarchy are formed by the rotation and the adding together of other images made up of fewer projections. The low computational cost of the algorithm depends on the efficient sampling of the intermediate images in the hierarchy. Understanding the algorithm within the signal processing framework, a general scheme for sampling an image made up of projections of arbitrary geometries is introduced. While the algorithm is related to one by Nilsson [2], the Fourier domain understanding leads to a more efficient sampling scheme for the intermediate images.

AB - We introduce a fast algorithm for backprojecting images from tomographic fan-beam projections that aggregates the projections in a hierarchical structure and achieves a computational cost of O(N 2 log P), when backprojecting an N × N pixel image from P projections. Like in the parallel-beam algorithm in [1], the images in the hierarchy are formed by the rotation and the adding together of other images made up of fewer projections. The low computational cost of the algorithm depends on the efficient sampling of the intermediate images in the hierarchy. Understanding the algorithm within the signal processing framework, a general scheme for sampling an image made up of projections of arbitrary geometries is introduced. While the algorithm is related to one by Nilsson [2], the Fourier domain understanding leads to a more efficient sampling scheme for the intermediate images.

UR - http://www.scopus.com/inward/record.url?scp=33750954356&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750954356&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33750954356

SN - 0780395778

SN - 9780780395770

T3 - 2006 3rd IEEE International Symposium on Biomedical Imaging: From Nano to Macro - Proceedings

SP - 1188

EP - 1191

BT - 2006 3rd IEEE International Symposium on Biomedical Imaging

ER -