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


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
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

CONTACT Dr. Williams