Computational Complexity – Biomedical Imaging Division, VT / WFU School of Biomedical Engineering and Sciences
http://www.bid.sbes.vt.edu
Biomedical Imaging Division, VT / WFU SBESSun, 27 Mar 2016 22:44:19 +0000en-UShourly1https://wordpress.org/?v=4.5.2Ye YB, Wang G, Zhu JH: Linear Diophantine equations for discrete tomography. Journal of X-Ray Science and Technology 10:59-66, 2002
http://www.bid.sbes.vt.edu/2001/01/ye-yb-wang-g-zhu-jh-linear-diophantine-equations-for-discrete-tomography-journal-of-x-ray-science-and-technology-1059-66-2002/
http://www.bid.sbes.vt.edu/2001/01/ye-yb-wang-g-zhu-jh-linear-diophantine-equations-for-discrete-tomography-journal-of-x-ray-science-and-technology-1059-66-2002/#respondMon, 01 Jan 2001 18:00:53 +0000http://localhost/wordpress/?p=476In 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 log22 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 log22 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. Click here for full article….
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