Bounds for discrete tomography solutions

Details Bounds for discrete tomography solutions Bounds for discrete tomography solutions

2011-04-29

arxiv.org/abs/1104.5589v2

Mathematics

Combinatorics

Scientific paper

We consider the reconstruction of a function on a finite subset of $\mathbb{Z}^2$ 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 $\mathbf{Z}^2$. 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.

Affiliated with

Also associated with

No associations

Rating

Bounds for discrete tomography solutions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bounds for discrete tomography solutions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bounds for discrete tomography solutions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-17454