## EECS CSPL SEMINAR SERIES

FALL TERM 1999

R. Kakarala
#
Dr. Ramakrishna Kakarala

### Visiting Scholar to EECS Department

### On sabbatical leave from

### University of Auckland, New Zealand

### kakarala@eecs.umich.edu

Thursday, October 14

4:30 - 5:30 P.M.

Room 1311 EECS

###
A Multiresolution form of the SVD and its applications to
image analysis

Abstract-

In many applications (e.g, image compression) it is useful to
obtain a statistical characterisation of an image, at each
of several levels of resolution. For this purpose, a
multiresolution form of the singular value decomposition
(SVD) is proposed. It is well known that a SVD decomposes a
matrix into orthogonal components with which optimal subrank
approximations may be obtained. The multiresolution SVD
proposed here retains those properties, and moreover, has
linear computational complexity. By using the
multiresolution SVD, the following important characteristics
of an image may be measured, at each of several levels of
resolution: isotropy, sphericity of principal components,
self-similarity under scaling, and resolution of
mean-squared-error into meaningful components. Theoretical
calculations are provided for simple statistical models to
show what might be expected. Results on real images are
provided to illustrate the usefulness of the multiresolution
SVD.

Biosketch-

R. Kakarala is currently a Visting Scholar with the EECS
Dept, on sabbatical leave from the University of Auckland.
He is a graduate of U. Michigan (B.S. 1986, M.S. 1988), and
of U. California, Irvine (PhD 1992). His research interests
are in image and video compression, statistical signal
processing, and computer vision. His home page is
here

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