Algorithms for linear time reconstruction by discrete tomography II

The reconstruction of an unknown function $f$ from its line sums is the aim discrete tomography. However, two main aspects prevent being easy task. In general, many solutions are allowed due to presence switching functions. Even when uniqueness conditions available, results about NP-hardness algorithms make their implementation inefficient values in certain sets. We show that this not case takes a field or unique factorization domain, such as $\R$ $\Z$. present linear time algorithm (in number directions and size grid), which outputs original for all points outside domains. Freely chosen assigned other points, namely, those with ambiguities. Examples provided.