Symmetry-constrained signal reconstruction from spherically averaged Fourier transform intensities
Abstract
Three dimensional signal reconstruction from averaged Fourier transform intensities is of great interest in many signal processing problems. Because of the information lost in the averaging, a priori knowledge about the signal plays a crucial role in the reconstruction. We investigate one problem of this type in which the averaging process is spherical averaging and the a priori knowledge is knowledge that the reconstructed object has certain symmetries. This type of problem occurs in the reconstruction of the three dimensional structure of a virus from solution x-ray scattering data. Our major achievements in this work are the following: (1) We derived new analytical functions to represent the complicated three dimensional symmetries of the virus. (2) We proposed and analyzed two parametric models for the three dimensional structure of the virus and used maximum likelihood methods to estimate the parameters in the models. (3) We further proposed and analyzed a non-parametric model and with it an iterative set projection algorithm for estimating the three dimensional viral structure. The analysis includes proof of the convergence properties of the algorithm. For each of these contributions we have developed the appropriate numerical and symbolic software. These ideas, as implemented in our software, have resulted in excellent three dimensional reconstructions of Cowpea Mosaic Virus from both simulated and experimental solution x-ray scattering data. Our contributions have opened exciting new opportunities for structural biologists to study new biological phenomena, such as dynamic processes of viruses.
Degree
Ph.D.
Advisors
Doerschuk, Purdue University.
Subject Area
Electrical engineering|Biophysics|Optics
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.