Journal article
Linear diophantine equations for discrete tomography
Journal of X-ray science and technology, Vol.10(1-2), pp.59-66
01/01/2002
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 super(2) sub(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 super(2) sub(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.
Details
- Title: Subtitle
- Linear diophantine equations for discrete tomography
- Creators
- Yangbo YeGe WangJiehua Zhu
- Resource Type
- Journal article
- Publication Details
- Journal of X-ray science and technology, Vol.10(1-2), pp.59-66
- ISSN
- 0895-3996
- eISSN
- 1095-9114
- Language
- English
- Date published
- 01/01/2002
- Academic Unit
- Mathematics
- Record Identifier
- 9984241057102771
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