Dr. Jamylle Laurice Carter


Prefix: Dr.
First Name: Jamylle
Middle Name: Laurice
Last Name: Carter


Degree: Ph.D.
Graduation Year: 2001

College: Harvard
Degree: B.A.
Graduation Year: 1992
Major: Mathematics

College: UCLA
Degree: M.A.
Graduation Year: 1998
Major: Mathematics


Birthplace:  Detroit, MI and raised in Montgomery, AL.


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. 



Year Born: 1971