Discrete tomography is a typical Inverse type Problem. In terms of (0,1) matrices it

is to reconstruct the matrix given the row and column weights. The known hypergraph degree sequence problem (C. Berge) is an equivalent form of the discrete tomography. Simple description of the set of all solutions is given in terms of monotone Boolean functions and ideals and filters of the partially ordered sets. Gradient algorithm with optimal steps is synthesized that constructs in general an approximate solution.