University of Illinois Urbana-Champaign

Double diffraction of quasiperiodic structures and bayesian image reconstruction

Xu, Jian

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https://hdl.handle.net/2142/31397

Description

Title
Double diffraction of quasiperiodic structures and bayesian image reconstruction
Author(s)
Xu, Jian
Issue Date
2006
Doctoral Committee Chair(s)
Hubler, Alfred W.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • quasiperiodic structures
  • quasiperiodic pulse
  • double diffraction
  • Bayesian Image Reconstruction
Language
en
Abstract
We study the spectrum of quasiperiodic structures by using quasiperiodic pulse trains. We find a single sharp diffraction peak when the dynamics of the incident wave matches the arrangement of the scatterers, that is, when the pulse train and the scatterers are in resonance. The maximum diffraction angle and the resonant pulse train determine the positions of the scatterers. These results may provide a methodology for identifying quasicrystals with a very large signal-tonoise ratio. We propose a double diffraction scheme to identify one-dimensional quasiperiodic structures with high precision. The scheme uses a set of scatterers to produce a sequence of quasiperiodic pulses from a single pulse, and then uses these pulses to determine the structure of the second set of scatterers. We find the maximum allowable number of target scatterers, given an experimental setup. Our calculation confirms our simulation results. The reverse problem of spectroscopy is reconstruction , that is, given an experimental image, how to reconstruct the original as faithfully as possible. We study the general image reconstruction problem under the Bayesian inference framework. We designed a modified multiplicity prior distribution, and use Gibbs sampling to reconstruct the latent image. In contrast with the traditional entropy prior, our modified multiplicity prior avoids the Sterling's formula approximation, incorporates an Occam's razor, and automatically adapts for the information content in the noisy input. We argue that the mean posterior image is a better representation than the maximum a posterior (MAP) image. We also optimize the Gibbs sampling algorithm to determine the high-dimensional posterior density distribution with high efficiency. Our algorithm runs N 2 faster than traditional Gibbs sampler. With the knowledge of the full posterior distribution, statistical measures such as standard error and confident interval can be easily generated. Our algorithm is not only useful for image reconstruction, it is useful for any Monte-Carlo algorithms in the Bayesian inference.
Type of Resource
text
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http://hdl.handle.net/2142/31397
Copyright and License Information
©2006 Xu

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