M.C. Escher illustrated his mathematical investigations of the constructive elements of this world in a form of two-dimensional drawings, which inspired many computer scientists to make computer reproductions and reconstructions. We introduce unusual higher-dimensional computer reconstructions to illustrate our research results in geometric modeling problems arising from analysis of Escher’s ar...

We study the shape reconstruction of an inclusion from faraway measurement associated electric field. This is inverse problem practical importance in biomedical imaging and known to be notoriously ill-posed. By incorporating Drude’s model permittivity parameter, we propose a novel scheme by using plasmon resonance with significantly enhanced resonant conduct delicate sensitivity analysis establ...

Abstract. We use optimal rational approximations of projection data collected in X-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the me...

We will study whether it is possible to regain information about a vector eld from projections, in the same way as is possible for scalar functions with Radon transform. It turns out that the curl and divergence of the eld can be reconstructed separately from two different transforms, and algorithms are devised using a variant of the ltered back projection algorithm for reconstruction. It is a ...