Brown Bag Seminar
The brown bag seminar is a weekly meeting organized by and for graduate students. The goal of the brown bag is to encourage students to practice presenting their work by giving talks to each other in a casual setting.
DateFriday, March 2, 2018 - 12:00pm
MCMC for High Energy X-Ray Radiography
DateFriday, March 16, 2018 - 12:00pm
AbstractImage deblurring via deconvolution can be formulated as a hierarchical Bayesian inverse problem, and numerically solved by Markov Chain Monte Carlo (MCMC) methods. Numerical solution is difficult because • inconsistent assumptions about the data outside of the field of view of the image lead to artifacts near the boundary; and • the Bayesian inverse problem is high-dimensional for high-resolution images. The numerical MCMC framework I present addresses these issues. Boundary artifacts are reduced by reconstructing the image outside the field of view. Numerical difficulties that arise from high-dimensions are mitigated by exploiting sparse problem structure in the prior precision matrix.
RF Gradient Index Devices and the Application of Mathematical Optics
DateFriday, March 23, 2018 - 12:00pm
AbstractThe introduction of metamaterials has enabled the design of a wide array of novel radio frequency (RF) devices. In this talk, the techniques of Mathematical Optics will be utilized for synthesis and analysis of dielectric-only gradient index metamaterial devices. The application of a WKB approximation to Maxwell’s equations will be shown to yield a Lagrangian formulation of optics. This formalism will be applied to the design of a gradient index zero order Quasi-Bessel beam lens. The synthesis of the lens requires solution of an integral equation of Abel’s type. Ray tracing of the resulting index distribution is difficult due to the presence of singularities, but may be accomplished by the clever application of numerical methods.