Shocks and other nonlinear filtering applied to image processing
Stanley Osher, Lenny I. Rudin · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1991
Two new filters for image enhancement are developed, extending the early work of the authors. One filter uses a new nonlinear time dependent partial differential equation and its discretization, the second uses a discretization which constrains the backwards heat equation and keeps it variation bounded. The evolution of the initial image as t increases through U(x,y,t) is the filtering process. The processed image is piecewise smooth, nonoscillatory and apparently an accurate reconstruction. The algorithms are fast and easy to program.