A method for derivation of inversion formulas for the Radon transform of f (x) is given. This method allows one to construct functions ψ(x) which are easy to compute and which have the same wave fronts as f (x). This, in turn, allows one to calculate the singular support S of f (x) by computing ψ(x) given tomographic data. A simple geometrical relation between the singular supports of f andˆf ,...

The significance of discontinuities frequently found in freeze-fracture replicas of the tight junction was evaluated using complementary replicas of hepatocyte junctions from control and bile duct-ligated rats. An extensive analysis of complementary replicas using rotary platinum shadowing indicates that discontinuities in the protoplasmic (P) fracture face do not represent structural breaks in...

We survey some recent results on the reconstruction of discontinuities by boundary measurements for elasticity and related systems in two dimensions. Our main tool is a new type of complex geometrical optics solutions.

We introduce a new texture representation that combines standard sampling, to be bilinearly interpolated in smoothly varying regions, with customizable discontinuities, to model sharp boundaries between these regions. The structure consists of a standard signal texture, plus a second texture we call pinchmap, which encodes discontinuities along generally curved lines; at rendering time the frag...

Abstract The ground conditions beyond an excavation face, especially discontinuities in rock masses, have a significant influence on tunnel construction. However, the actual observed during construction are often different from predicted geotechnical site explorations carried out design stage. Changes may require alterations design, leading to substantial disruptions schedule and budget. In thi...