Adaptive Reconstruction of Discrete-Valued Objects from few Projections

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.