Analysis and Applications of Stochastic Sampling Strategies

I will summarise my understanding and analysis of two classes of problems whose manifestations are encountered across various engineering disciplines. The first of these two classes, which I will allude to as "the reconstruction problem", involves hypothesising functions over multi-dimensional domains given a limited sets of observations (or
samples) of the functions. Then, I will present my recent analysis of numerical integration for potentially high-dimensional, non-stationary, discontinuous integrands. Further, in the context of digital image synthesis, I will explain how these two problems manifest themselves in the light transport problem and present stochastic sampling strategies for improving the efficiency of simulations of geometric light transport.

My presentation will consist of three sections, of roughly 15 minutes each. First, I will formulate the abstract problems and summarise some of my recent results. Next, I hope to encourage members of the audience to identify these abstract problems in the context of their own research problems. Finally, I will present an application (synthesising computer graphics imagery) of the light transport problem to exemplify the amalgamation of analysis, insight and practical sampling strategies towards a concrete goal.