[lug] DIRECT BLIND DECONVOLUTION AND LEVY PROBABILITY DENSITIES

[Wayde Allen]

MCSD Boulder Colloquium 

DATE:       Thursday June 22 2000

TIME:       11 AM 

LOCATION:   Room 1-4536

SPEAKER:    Alfred S. Carasso

FROM:       Mathematical and Computational Sciences Division,
            National Institute of Standards and Technology,
            Gaithersburg, MD 20899. 

E-MAIL:     alfred.carasso at nist.gov

TITLE:      DIRECT BLIND DECONVOLUTION AND LEVY PROBABILITY DENSITIES.



ABSTRACT:

Blind deconvolution seeks to deblur an image without knowing the 
cause of the blur. Iterative methods are commonly applied to that 
problem, but the iterative process is slow, uncertain,  and often 
ill-behaved. This talk considers a significant but limited class 
of blurs that can be expressed as convolutions of 2-D symmetric 
Levy `stable' probability density functions. This class includes 
and generalizes Gaussian and Lorentzian distributions. For such
blurs, methods are developed that can detect the point spread 
function from 1-D Fourier analysis of the blurred image. A separate
image deblurring technique uses this detected point spread function 
to deblur the image. Each of these two steps uses direct non-iterative 
methods, and requires interactive adjustment of parameters. As a 
result, blind deblurring of 512X512 images can be accomplished in 
minutes of CPU time on current desktop workstations.  Numerous blind 
experiments on synthetic data show that for a given blurred image, 
several distinct point spread functions may be detected that lead to
useful, yet visually distinct reconstructions. Application to real 
blurred images will also be demonstrated.


BIOGRAPHICAL INFORMATION:

Alfred Carasso received the Ph.D. degree in mathematics at the
University of Wisconsin in 1968. He was a professor of mathematics
at the University of New Mexico and a consultant at Los Alamos,
prior to joining the National Institute of Standards and Technology
as a research mathematician in 1982. His interests lie primarily in
the mathematical and computational analysis of ill-posed continuation
problems in partial differential equations.