Numerical scheme for solving the acoustical inverse scattering problem

Frank Wuebbeling; Frank Natterer

doi:10.1117/12.284719

9 December 1997 Numerical scheme for solving the acoustical inverse scattering problem

Frank Wuebbeling, Frank Natterer

Proceedings Volume 3171, Computational, Experimental, and Numerical Methods for Solving Ill-Posed Inverse Imaging Problems: Medical and Nonmedical Applications; (1997) https://doi.org/10.1117/12.284719
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

In current public discussions, much attention is paid to the danger of breast cancer. X-ray methods for cancer detection like mammography are sometimes considered inappropriate. Recently, novel optical and acoustical methods are being examined. One of these is image reconstruction from time- harmonic ultrasound data, which requires determining the coefficient f in the Helmholtz equation (Delta) u + k²(l + f)u equals 0 from boundary measurement of various solutions u of the equation for different boundary conditions. In this equation, f determines the physical properties of the scatterer, while k is the wave number and u is the time-harmonic sound wave. Born- and Rytov- approximations have been used for some time to accomplish this task, but are not precise enough. All functions may be either a 2D or a 3D function, depending on the application. To overcome the complexity problems, an iterative algorithm that works on finite data and incorporates finite boundary conditions instead of radiation condition will be presented. Two main ingredients are used to accomplish this. First, an adjoint-field type iteration scheme is employed. Second, an initial value solver is used to solve the direct problem of computing a sound wave, given boundary conditions and a scatterer. The algorithm allows us to solve the problem with realistic parameters for simulated data on regular workstations in a few minutes.

Citation Download Citation

Frank Wuebbeling and Frank Natterer "Numerical scheme for solving the acoustical inverse scattering problem", Proc. SPIE 3171, Computational, Experimental, and Numerical Methods for Solving Ill-Posed Inverse Imaging Problems: Medical and Nonmedical Applications, (9 December 1997); https://doi.org/10.1117/12.284719

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
8 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Inverse scattering problem

Breast cancer

Cancer

Computer simulations

Image restoration

Mammography

Ultrasonography

Show All Keywords

Keywords/Phrases

Search In:

Publication Years