Committee: 

Dr. Yezzi, Advisor

Dr. Vela, Chair

Dr. Romberg

Abstract: The objective of the proposed research is to apply the framework of PDE acceleration to variational formulations of inversion problems, optical flow, and stereo reconstruction. By posing these problems within well-known variational  frameworks, it is possible to apply a new technique known as Partial Differential  Equation (PDE) acceleration which excels at improving convergence in non-convex variational formulations. Our early work in more easily convexified inversion problems has shown robust performance against typical convex optimization methods such as Alternating Direction Method of Multipliers (ADMM) and Primal-Dual (PD). These experiments have been followed up by additional work in more non-convex arenas such as optical flow with planned extensions into variational stereo reconstruction.