Gaussian beam decomposition of high frequency wave fields using expectation-maximization

Authors:
Gil Ariel;Björn Engquist;Nicolay M. Tanushev;Richard Tsai
Affiliations:
Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel;Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, USA;Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, USA;Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, USA
Venue:
Journal of Computational Physics
Year:
2011

Citing 3
Cited 0

Numerical microlocal analysis of harmonic wavefields

Journal of Computational Physics
Gaussian beam decomposition of high frequency wave fields

Journal of Computational Physics
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing

SIAM Journal on Imaging Sciences

Quantified Score

Hi-index	31.45

Visualization

Abstract

A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation-maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are further refined by an optimization procedure that minimizes the difference between the Gaussian beam superposition and the highly oscillatory wave field in the energy norm.