Noise propagation in linear and nonlinear inverse scattering

Dilip N. Ghosh Roy, John Roberts, Matthias Schabel, Stephen J. Norton

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The propagation of noise from the data to the reconstructed speed of sound image by inverse scattering within the framework of the Lippmann-Schwinger integral equation of scattering is discussed. The inversion algorithm that was used consisted in minimizing a Tikhonov functional in the unknown speed of sound. The gradient of the objective functional was computed by the method of the adjoint fields. An analytical expression for the inverse scattering covariance matrix of the image noise was derived. It was shown that the covariance matrix in the linear x-ray computed tomography is a special case of the inverse scattering matrix derived in this paper. The matrix was also analyzed in the limit of the linearized Born approximation, and the results were found to be in qualitative agreement with those recently reported in the literature for Born inversion using filtered backpropagation algorithm. Finally, the applicability of the analysis reported here to the obstacle problem and the physical optics approximation was discussed.

Original languageEnglish (US)
Pages (from-to)2743-2749
Number of pages7
JournalJournal of the Acoustical Society of America
Volume121
Issue number5
DOIs
StatePublished - 2007
Externally publishedYes

Fingerprint

noise propagation
inverse scattering
inversions
physical optics
acoustics
S matrix theory
Born approximation
integral equations
tomography
gradients
propagation
matrices
approximation
scattering
x rays
Inversion
Approximation
Sound

ASJC Scopus subject areas

  • Acoustics and Ultrasonics

Cite this

Noise propagation in linear and nonlinear inverse scattering. / Ghosh Roy, Dilip N.; Roberts, John; Schabel, Matthias; Norton, Stephen J.

In: Journal of the Acoustical Society of America, Vol. 121, No. 5, 2007, p. 2743-2749.

Research output: Contribution to journalArticle

Ghosh Roy, Dilip N. ; Roberts, John ; Schabel, Matthias ; Norton, Stephen J. / Noise propagation in linear and nonlinear inverse scattering. In: Journal of the Acoustical Society of America. 2007 ; Vol. 121, No. 5. pp. 2743-2749.
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