Method of Formal Parameter Expansion for Acoustical Inverse Scattering Problems
In acoustical diffraction tomography, the inverse scattering perturbation theory, especially the first-order Born perturbation approximation has its advantages: comparatively simple calculations. That is why it has been used in diffraction tomography in many fields, such as in medical and seismic imaging 1−2. But this method has its disadvantages: severe limitations on scatterers, i.e., objects to be imaged3−5. These limitations are impracticable in the most cases, such as in medical imaging and petroleum exploration. The use of high-order, for example, second-order Born perturbation algorithms can reduce these limitations to a certain extent. But they also failed to reconstruct the object with good accuracy in many cases 5. In such cases, the third- or even higher-order Born approximation must be taken into ac- count. This will result in more and more tedious calculations. Can and how do we find a method which needs comparatively simple calculations and has not severe limitations on objects?
KeywordsFourier Spectrum Helmholtz Equation Severe Limitation Inverse Scattering Scattered Field
Unable to display preview. Download preview PDF.
- M. Kaveh, M. Soumekh, and R.K. Mueller, A comparison of Born and Rytov approximations in acoustic tomography, in:” Acoustical Imaging, vol.11,” J. Powers, ed. Plenum, New York(1981).Google Scholar
- M. Kaveh, M. Soumekh, Zhen-Qiu Lu, R.K. Mueller, and J.F. Greenleaf, Further results on diffraction tomography using Rytov approximation, in: ”Acoustical Imaging, vol.12,” E.A. Ash and K. Hill, eds. Plenum, New York(1982).Google Scholar
- I.M. Gel’fand and G.E. Shilov, ”Generalized Functions (Vol.1),” Academic, New York(1964).Google Scholar