Adaptive Bayesian Signal Reconstruction with A Priori Model Implementation and Synthetic Examples for X-Ray Crystallography

Abstract

A signal reconstruction problem motivated by X-ray crystallography is (approximately) solved in a Bayesian statistical approach. The signal is zero-one, periodic, and substantial statistical a priori information is known, which is modeled with a Markov random field. The data are inaccurate magnitudes of the Fourier coefficients of the signal. The solution is explicit and the computational burden is independent of the signal dimension. In this paper, a detailed parameterization of the a priori model appropriate for crystallography is proposed and symmetry-breaking parameters in the solution are used to perform data-dependent adaptation of the estimator. The adaptation attempts to minimize the effects of the spherical model approximation used in the solution. Several examples in one and two dimensions based on simulated data are presented.

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Document Details

Document Type
Technical Report
Publication Date
Feb 26, 1991
Accession Number
ADA459539

Entities

People

  • Peter C. Doerschuk

Organizations

  • Purdue University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Computations
  • Crystallography
  • Data Science
  • Electrical Engineering
  • Electron Density
  • Electrons
  • Engineering
  • Estimators
  • Fourier Series
  • Inverse Problems
  • Probability
  • Random Variables
  • Statistics
  • Two Dimensional
  • X Rays
  • X-Ray Crystallography

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms