Dissertation/Thesis Abstract

Mathematical models and numerical methods for wavefront reconstruction
by Chu, Qing, Ph.D., Emory University, 2013, 118; 3614311
Abstract (Summary)

Obtaining high resolution images of space objects from ground based telescopes is challenging, and often requires computational post processing methods to remove blur caused by atmospheric turbulence. In order for an image deblurring (deconvolution) algorithm to be effective, it is important to have a good approximation of the blurring operator. In space imaging, the blurring operator is defined in terms of the wavefront of light, and how it is distorted as it propagates through the atmosphere. In this thesis we consider new mathematical models and algorithms to reconstruct the wavefront, which requires solving a large scale ill-posed inverse problem. We show that by exploiting and fusing information from multiple measurements, we are able to obtain better reconstructed wavefronts than existing methods. In addition, to fulfill the large scale requirement for astronomical uses, we present results of a parallel implementation utilizing the Trilinos project, a mathematical software library for solving problems from many academic and research fields. Moreover, we study an symmetric successive over-relaxation (SSOR) preconditioner for this image reconstruction problem. Numerical results for different image reconstruction systems under variety of seeing conditions indicate good behavior of the SSOR preconditioner with respect to iteration numbers and computational time.

Indexing (document details)
Advisor: Nagy, James
Commitee: Benzi, Michele, Gao, Hao, Jefferies, Stuart, Veneziani, Alessandro
School: Emory University
Department: Math and Computer Science
School Location: United States -- Georgia
Source: DAI-B 75/06(E), Dissertation Abstracts International
Subjects: Applied Mathematics, Mathematics
Keywords: Astronomical imaging, Image deblurring, Inverse problems, Wavefront reconstruction
Publication Number: 3614311
ISBN: 9781303793967