Jamylle L. Carter
place: born in Detroit, MI and raised in Montgomery, AL.
A.B., Mathematics, Harvard, 1992; M.A., Mathematics, UCLA, 1994; C. Phil. in Mathematics, 1998.
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/
Fall 2004Postdoctoral Associate at the Institute for Mathematics and its Applications at the University of Minnesota
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.
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