## Abstract

In this report, we present a number-theory-based approach for discrete tomography (DT), which is based on parallel projections of rational slopes. Using a well-controlled geometry of X-ray beams, we obtain a system of linear equations with integer coefficients. Assuming that the range of pixel values is a(i, j) = 0, 1,..., M - 1, with M being a prime number, we reduce the equations modulo M. To invert the linear system, each algorithmic step only needs log_{2}^{2} M bit operations. In the case of a small M, we have a greatly reduced computational complexity, relative to the conventional DT algorithms, which require log_{2}^{2} N bit operations for a real number solution with a precision of 1/N. We also report computer simulation results to support our analytic conclusions.

Original language | English |
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Pages (from-to) | 59-66 |

Number of pages | 8 |

Journal | Journal of X-Ray Science and Technology |

Volume | 10 |

Issue number | 1-2 |

State | Published - 2002 |

## Keywords

- Computational complexity
- Computed tomography (CT)
- Diophantine equations
- Discrete tomography (DT)
- Number theory