We consider the reconstruction of a function on a finite subset of
Z2 if the line sums in certain directions are prescribed. The real
solutions form a linear manifold, its integer solutions a grid. First we
provide an explicit expression for the projection vector from the origin onto
the linear solution manifold in the case of only row and column sums of a
finite subset of Z2. Next we present a method to estimate the
maximal distance between two binary solutions. Subsequently we deduce an upper
bound for the distance from any given real solution to the nearest integer
solution. This enables us to estimate the stability of solutions. Finally we
generalize the first mentioned result to the torus case and to the continuous
case