Some Vibrating Membrane Equations for the Linear Estimation of Two-Dimensional Isotropic Random Fields,

Abstract

This paper considers the problem of estimating a two-dimensional isotropic random field given some noisy observations of this field over a disk of finite radius. By expanding the field and observations in Fourier series, and exploiting the covariance structure of the resulting Fourier coefficient processes, some vibrating equations are obtained for estimating the random field. These equations provide a set of recursions for constructing the field estimates as the radius of the observation disk increases. In the spectral domain, these recursions take the form of Schrodinger equations which can be viewed as being associated to an inverse scattering problem. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1982
Accession Number
ADA116959

Entities

People

  • Bernard C. Lévy
  • John N. Tsitsiklis

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Angular Momentum
  • Differential Equations
  • Equations
  • Filtration
  • Fourier Series
  • Hilbert Space
  • Integral Equations
  • Inverse Scattering
  • Mathematical Filters
  • Partial Differential Equations
  • Quantum Mechanics
  • Random Variables
  • Schrodinger Equation
  • Stationary Processes
  • Statistics
  • Stochastic Processes
  • Two Dimensional

Readers

  • Aerosol Science/Aerosol Physics
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.