Project: Imaging through atmospheric turbulence: acquisition, simulation and restoration 
In the past decade several different longrange imaging systems were developed. A direct consequence of imaging distant scenes are the atmosphere effects, and especially the presence of turbulence, which become nonnegligible and affect the final resolution. Several image processing algorithms were proposed to reduce the impact of the atmosphere and to reconstruct an image with better resolution and without geometrical deformation.
In this REU project, the team will be split to work on several aspects of the atmospheric turbulence chain. 


Project: Analysis of Markov chain Monte Carlo algorithms for Bayesian statistical models 
Bayesian statistical methods have become popular and their use continues to grow in the applied sciences. This increase in popularity is largely due to the availability of Markov chain Monte Carlo (MCMC) algorithms which allow for the estimation of quantities associated with posterior distributions. The goal of this REU project is to study the performance of several MCMC algorithms associated with (simplified versions of) popular Bayesian statistical models. Knowledge of Bayesian statistics, Markov chains, or the Rstatistical software is helpful but not required. 

 Project Director: Jérôme Gilles 
Dr. Gilles is Professor in the Department of Mathematics and Statistics at SDSU since 2014 and was Assistant Adjunct Professor in the Department of Mathematics at UCLA from 2010 to 2014 where he led several REU projects. From 2001 to 2010, he worked for the French Ministry of Defense as an image processing expert where he started to work on atmospheric turbulence restoration problems. Dr. Gilles' interests are applied harmonic/functional analysis and their applications in signal and image processing. 


Project Director: Jorge Carlos Román   
Dr. Román is a new assistant professor in the Department of Mathematics and Statistics at SDSU. He obtained his PhD in Statistics from University of Florida in 2012 and was a (nontenure track) assistant professor in the Department of Mathematics at Vanderbilt University (20122015). Dr. Román's research interests are Bayesian statistics and Markov chain Monte Carlo algorithms. 

 Program Director: Vadim Ponomarenko 
Dr. Ponomarenko has been directing undergraduate and REU research for 17 years. Most REU participants he has worked with have been coauthors on at least one paper as a result of this collaboration. 
Projects from previous years: 2007, 2008, 2009, 2012, 2013, 2014