TY - JOUR

T1 - Linear Diophantine Equations for Discrete Tomography

AU - Ye, Yangbo

AU - Wang, Ge

AU - Zhu, Jiehua

N1 - 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 coe

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - Discrete tomography

KW - Linear diophantine equations

UR - https://content.iospress.com/articles/journal-of-x-ray-science-and-technology/xst00057

M3 - Article

SN - 0895-3996

VL - 10

JO - Journal of X-Ray Science and Technology

JF - Journal of X-Ray Science and Technology

ER -