Projects
Code is on GitHub.
Ongoing
Deformable Image Registration with Learned Proximal Networks (LPNs) Python
We study 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. We analyze the convergence of the resulting PnP proximal gradient and ADMM schemes for the nonconvex registration objective, propose a variant that yields diffeomorphic transformations by construction, and evaluate the approach on synthetic and 3D neuroimaging data in comparison to ANTs.
Learned Proximal Networks for High-Dimensional Hamilton–Jacobi PDEs Python
Building on Fang, Buchanan and Sulam (ICLR 2024). The method learns a convex potential whose gradient is the proximal operator, then recovers the prior by fitting a second network or by using just one network when the proximal operator is available.
Other Projects
Nonlinear Optimization MATLAB
Implementations of line-search and trust-region methods for smooth nonlinear optimization — steepest descent, modified Newton, truncated Newton-CG, Cauchy-point, SR1, and Moré–Sorensen solvers — benchmarked on seven test problems with convergence plots, per-iteration logs, and a written report.
Scientific Computing in Python Python
Numerical methods across ordinary differential equations, numerical linear algebra, data assimilation, data-driven optimization, and financial mathematics.