Jamylle L. Carter

Born: 1971

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.

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.

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