My dissertation, PDEs and Machine Learning with Applications in Medical Imaging, develops optimization methods with provable guarantees and applies them to inverse problems and imaging. Current work learns proximal operators with input-convex neural networks and connects them to Hamilton–Jacobi equations, giving a route to reconstruction that avoids solving an optimization problem at every query. An ongoing project carries these ideas into medical image registration, studying plug-and-play (PnP) algorithms for deformable image registration in which the regularizer is supplied by a learned proximal network (LPN), i.e., a neural network that is, by construction, the exact proximal operator of a (possibly nonconvex) learned regularization functional.

• DSCI 311: Optimization and Mathematical Foundations for Data Science

• MTH 101, 102, 104 General Mathematics I, II, III
• MTH 201 Mathematical Methods
• MTH 202 Differential Equation I
• MTH 203 Set, Logic and Algebra
• MTH 204 Linear Algebra I
• SEN 203 Discrete Structures
• MAT 001 Advanced Calculus