Computational and Applied Math Proseminar

Department of Mathematics, Arizona State University

Thurday, August 30, 2001, 12:15 p.m. in GWC Room 604

Anne Gelb

Department of Mathematics

Reducing the Effects of Noise in Image Reconstruction

Abstract Fourier spectral methods have proven to be powerful tools that are frequently employed in image reconstruction. However, since images can be typically viewed as piecewise smooth functions, the Gibbs phenomenon often hinders accurate reconstruction. Much work has been done to combat the Gibbs phenomenon, including the development of numerical edge detection methods as well as reconstruction techniques that effectively reduce the Gibbs oscillations while maintaining high resolution accuracy at the edges.

While the Gibbs phenomenon is a standard obstacle for the recovery of all piecewise smooth functions, in many image reconstruction problems there is the additional impediment of random noise existing within the spectral data. This paper addresses the issue of noise in image reconstruction and its effects on the ability to locate the edges and recover the image. The resulting numerical method not only recovers piecewise smooth functions with very high accuracy, but it is also robust in the presence of noise.

For further information please contact: mittelmann@asu.edu