Thursday,
April 24, 2003, 12:15 p.m. in GWC Room 604
Wolfgang Stefan
Department of Mathematics and Statistics
Image Restoration by Blind Deconvolution
Abstract
The goal of image restoration by blind deconvolution is to find uncorrupted
images from noisy, blurred ones. In the deconvolution approach the blurred
image f is supposed to be the result of a convolution of the original
image g and a known or unknown point spread function (psf) h i.e.
f=g*h+noise. In case of an unknown psf the deconvolution is referred to as
"blind deconvolution".
In some cases the point spread function h is known, at least in some
statistical sense. However in most cases like PET or MRI images the psf is
unknown. Even when the psf is known, the solution of the inverse problem,
namely obtaining g given h and f, is not well posed. This means that some
additional information about the image
has to be used to "regularize" this problem. This might include information
about the support of the original image or the smoothness of
the image. Similar information may be used for the psf, when one also desires
to find g, and h, from the signal f. Based on simulation with 1d data, we
expect that this technique not only results in sharper images, but it also
dramatically reduces the noise in a given signal.
