Jamylle L. Carter
Born: 1971
place: born in Detroit, MI and raised in Montgomery, AL.
.education.gif){kind=small}
A.B., Mathematics,
Harvard, 1992; M.A., Mathematics, UCLA, 1994; C. Phil. in Mathematics,
1998.
Ph.D. Mathematics
University of California, Los Angeles (2001)
thesis: Dual Methods for Total Variation-Based Image Restoration
(Tony Chan)
area of degree:
January 2005 postdoctoral fellowship at the Mathematical Sciences Research Institute in Berkeley, California
personal or universal URL: http://silver.ima.umn.edu/~jcarter/
or http://www.ima.umn.edu/~jcarter
email: jcarter@msri.org
Fall 2004Postdoctoral Associate at the Institute for Mathematics and its Applications at the University of Minnesota
RESEARCH
Description of Jamylle's research for the 2000 Clay Mathematical
Liftoff Fellowship: The goal of image restoration is to extract
the clearest image possible from a distorted image. We seek a
solution in the form of a smooth, non-oscillatory function that
best matches the corrupted image while preserving its edges. A
technique known as Tikhonov regularization imposes smoothness
requirements on the restored image. Total Variation regularization
is edge-preserving: it allows discontinuous solutions which best
fit the noisy image. In its primal form, the Total Variation problem
is an unconstrained optimization problem with a non-smooth objective
function. To make the objective function differentiable, previous
methods have required the use of a small perturbation parameter.
We circumvent the need for a perturbation parameter by solving
the dual formulation of the Total Variation problem, which yields
a quadratic objective function with inequality constraints. We
have implemented a barrier method, and we are developing a hybrid
algorithm which switches between the primal and dual formulations.
back to Black Women in the Mathematical Sciences
The website
MATHEMATICIANS OF THE
AFRICAN DIASPORA
are brought to you by
The Mathematics Department of
The State University of New York at Buffalo.
They are created and maintained by
Scott W. Williams
Professor of Mathematics
