An efficient algorithm for reconstructing binary matrices from horizontal and vertical absorbed projections

This paper studies the classical tomographical problem of the reconstruction of a binary matrix from projections in presence of absorption. In particular, we consider two projections along the horizontal and vertical directions and the mathematically interesting case of the absorption coefficient β0=1+52. After proving some theoretical results on the switching components, we furnish a fast algorithm for solving the reconstruction problem from the horizontal and vertical absorbed projections. As a significative remark, we obtain also the solution of the related uniqueness problem.