My thesis advisor is Prof. Roummel F. Marcia who works in nonlinear nonconvex optimiation, mathematical signal processing and numerical linear algebra.

Recently we derived the compact representation for matrices belonging to the full Broyden class of quasi-Newton updates, where each update may be either rank-one or rank-two. In this representation it is not assumed the same Broyden update is used each iteration; rather, different members of the Broyden class may be used each iteration. A practical implementation of the compact representation was also implemented using MATLAB. Furthermore, we demonstrate how to compute the compact representation for the inverse of these matrices, as well as a practical algorithm for solving linear systems with members of the Broyden class of updates. This work is in collaboration with Prof. Jennifer B. Erway.

I have also been working in collaboration with Dr. Lasith Adhikari to extend his previous results on sparse reconstruction for fluorescence lifetime imaging microscopy with Poisson noise. The problem involves reconstructing fluorophore sources using a sparsity promoting non-convex optimization method known as SPIRAL-$$\ell_p$$.