Recursive Linear Smoothing for the 2-D Helmholtz Equation.

Abstract

A fast algorithm for reconstructing images governed by a 2-D Helmholtz equation is presented. The computational complexity of the algorithm is O(NMlogM) or O(N(M-sq) depending on boundary conditions, where N and M are the number of spatial grid points in the x and y directions respectively. This problem arises when smoothing a large number of images governed by the 2-D wave equation, because a Fourier transform in time gives a new set of images governed by the Helmholz equation. When the images come from a scattering process, we show that a linear least-squares Born inversion of the wave field amplitudes can be performed during the smoothing procedure without changing the computational complexity. The smoothing algorithm is well posed, and the sample functions of the smoothed estimate possess smoothness properties consistent with the Helmholtz equation.

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Document Details

Document Type
Technical Report
Publication Date
Sep 25, 1986
Accession Number
ADA179784

Entities

People

  • Howard L. Weinert
  • Laurence R. Riddle

Organizations

  • Johns Hopkins University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Acoustic Holography
  • Algorithms
  • Amplitude
  • Boundaries
  • Computational Complexity
  • Differential Equations
  • Dynamics
  • Equations
  • Fourier Series
  • Helmholtz Equations
  • Inversion
  • Linear Systems
  • Scattering
  • Time Domain
  • Two Dimensional
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis