| Περιγραφή: |
Summary: We present an heuristic furnishing a highly parallelizable algorithm to find an approximate reconstruction of an spatial binary function defined on a lattice, from the line sums of all parallel line in a few directions. This heuristic is derived from a Radon transform on vector spaces over finite fields proposed by the author [SIAM J. Matrix Anal. Appl. 9, No. 3, 393-398 (1988; Zbl 0651.65094), Mullen Gary L. (ed.) et al., Finite fields, coding theory, and advances in communications and computing. Proceedings of the international conference on finite fields, coding theory, and advances in communications and computing, held at the University of Nevada, Las Vegas, USA, August 7-10, 1991. New York: Marcel Dekker, Inc. (ISBN 0-8247-8805-2). Lect. Notes Pure Appl. Math. 141, 395-402 (1993; Zbl 0784.65096)] and \textit{A. Correa}, \textit{R. Cruz} and \textit{P. M. Salzberg} [On a spatial limited angle model for \(X \)-ray computerized tomography. Quinto, Eric Todd (ed.) et al., Tomography, impedance imaging and integral geometry. 1993 AMS-SIAM summer seminar, June 7-18, 1993, Mount Holyoke College, South Hadley, MA, USA. Providence, RI: American Mathematical Society, (ISBN 0-8218-0337-9/SC). Lect. Appl. Math. 30, 25-33 (1994)]. Some reconstruction are exhibited. |