Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9514648 | Electronic Notes in Discrete Mathematics | 2005 | 20 Pages |
Abstract
Recently, we proposed an algorithm for binary tomography based on DC (difference of convex functions) programming [T. Pham Dinh, L.T. Hoai An, A d.c. optimization algorithm for solving the trust-region subproblem, SIAM J. Optim. 8 (2) (1998) 476-505, T. Schüle, C. Schnörr, S. Weber, and J. Hornegger, Discrete Tomography by Convex-Concave Regularization and D.C. Programming, Technical Report 15/2003, Computer Science Series, University of Mannheim, Dec. 2003. To appear in Discrete Applied Mathematics, Elsevier]. In this paper, we extend the binary reconstruction problem to multi-valued objects. We describe how such objects can be reconstructed just by combining binary decisions. The proposed algorithm remains practicable for multi-valued reconstructions, and even with a large number of discrete values. Furthermore, we show how approximately known absorption levels can be adaptively estimated within the reconstruction process.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Thomas Schüle, Stefan Weber, Christoph Schnörr,