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

In this paper we consider the problem of reconstructing a binary matrix from absorbed projections, as introduced in [Kuba and Nivat, Linear Algebra Appl. 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.