Accession Number:

ADA179784

Title:

Recursive Linear Smoothing for the 2-D Helmholtz Equation.

Descriptive Note:

Interim rept.,

Corporate Author:

JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Report Date:

1986-09-25

Pagination or Media Count:

32.0

Abstract:

A fast algorithm for reconstructing images governed by a 2-D Helmholtz equation is presented. The computational complexity of the algorithm is ONMlogM or ONM-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.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE