This paper considers the problem of finding the set of MAP reconstructions of an N× N block conditioned on a boundary configuration consisting of 1 or 2 alternating runs of black and white in a uniform Ising model with no external field. It shows that when the boundary contains a single run, the set of minimum odd bond reconstructions are described by simple paths connecting the endpoints of either the black or white run. When the boundary consists of 2 runs, the set of minimum odd bond reconstructions are formed in one or more of the following ways: by simple paths connecting the endpoints of the two black runs; by simple paths connecting the two white runs; or by three simple paths connecting one of the boundary odd bonds to each of the other three. The paper provides a closed form solution for determining all minimum odd bond reconstructions for a 2-run boundary.
CITATION STYLE
Reyes, M. G., Neuhoff, D. L., & Pappas, T. N. (2020). MAP Interpolation of an Ising Image Block. In Advances in Intelligent Systems and Computing (Vol. 943, pp. 237–256). Springer Verlag. https://doi.org/10.1007/978-3-030-17795-9_17
Mendeley helps you to discover research relevant for your work.