Bounds for discrete tomography solutions

We consider the reconstruction of a function on a finite subset of Z2Z2 where the line sums in certain directions are prescribed. Its 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 Z2Z2. Next we present a method for estimating 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 result mentioned above to the continuous case.