An algorithm for the reconstruction of discrete sets from two projections in presence of absorption

In this paperwe consider the problemof reconstructing a binarymatrix fromabsorbedprojections, as introduced in [Kuba and Nivat, LinearAlgebraAppl. 339 (2001) 171–194]. In particular we prove that two left and right horizontal absorbed projections along a single direction uniquely determine a row of a binary matrix for a specific absorption coefficient. Moreover, we give a linear time algorithm which reconstructs such a row and we analyze its performances by determining the worst case complexity. Finally, we study the same problems in the presence of different absorption coefficients. © 2005 Elsevier B.V. All rights reserved.