Speaker: Alfred S. Carasso, National Institute of Standards and Technology
Title: BOCHNER SUBORDINATION, LOGARITHMIC DIFFUSION EQUATIONS, AND BLIND DECONVOLUTION OF HUBBLE SPACE TELESCOPE IMAGERY AND OTHER SCIENTIFIC DATA
Abstract:
Generalized Linnik processes and associated logarithmic diffusion
equations can be
constructed by appropriate Bochner randomization of the time variable in
Brownian motion and the
related heat conduction equation. Remarkably, over a large but finite frequency
range, generalized
Linnik characteristic functions can exhibit almost Gaussian behavior near the
origin, while behaving
like low exponent isotropic L´evy stable laws away from the origin. Such
behavior matches Fourier
domain behavior in a large class of real blurred images of considerable
scientific interest, including
Hubble space telescope imagery and scanning electron micrographs. This paper
develops a powerful
blind deconvolution procedure based on postulating system optical transfer
functions (otf) in the
form of generalized Linnik characteristic functions. The system otf and ~Qtrue~R
sharp image are
then reconstructed by solving a related logarithmic diffusion equation
backwards in time, using the
blurred image as data at time t = 1. The present methodology significantly
improves upon previous
work based on system otfs in the form of L´evy stable characteristic functions.
Such improvement
is validated by the substantially smaller image Lipschitz exponents that ensue,
confirming increased
fine structure recovery. These results resolve the unexplained appearance of
exceptionally low L´evy
stable exponents in previous work on the same class of images. The paper is
illustrated with striking
enhancements of gray scale and colored images.
[Click here for a sample.]
Place: Science and Technology Building I, Room 242
Refreshments will be served before the talk at 3:00 p.m. in Room 222.
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491