- 著者
- Ide T Isozaki H Nakata S Siltanen S
- 出版者
- Institute of Physics
- 雑誌
- Inverse problems (ISSN:02665611)
- 巻号頁・発行日
- vol.26, no.3, pp.035001, 2010-03
- 被引用文献数
- 12 12
Assume one is given a three-dimensional bounded domain with an unknown conductivity distribution inside. Further, suppose that the conductivity consists of a known background and unknown anomalous regions (inclusions) where conductivity values are unknown and different from the background. A method is introduced in Ide et al (2007 Commun. Pure Appl. Math. 60 1415–42) for locating inclusions approximately from noisy localized voltage-to-current measurements performed at the boundary of the body. The method is based on the use of complex geometrical optics solutions and hyperbolic geometry; numerical testing is presented in the aforementioned paper for the two-dimensional case. This work reports the results of computational implementation of the method in dimension three, where both the simulation of data and the computerized inversion algorithm are more complicated than in dimension two. Three new regularizing steps are added to the algorithm, resulting in significantly better robustness against noise. Numerical experiments are reported, suggesting that the approximate location of the inclusions can be reliably recovered from the data with a realistic level of measurement noise. Potential applications of the results include early diagnosis of breast cancer, underground contaminant detection and nondestructive testing.
- 著者
- Courdurier M Noo F Defrise M Kudo H
- 出版者
- Institute of Physics
- 雑誌
- Inverse problems (ISSN:02665611)
- 巻号頁・発行日
- vol.24, no.6, pp.065001, 2008-12
- 被引用文献数
- 92 80
A case of incomplete tomographic data for a compactly supported attenuation function is studied. When the attenuation function is a priori known in a subregion, we show that a reduced set of measurements are enough to uniquely determine the attenuation function over all the space. Furthermore, we found stability estimates showing that reconstruction can be stable near the region where the attenuation is known. These estimates also suggest that reconstruction stability collapses quickly when approaching the set of points that is viewed under less than 180°. This paper may be seen as a continuation of the work 'Truncated Hilbert transform and image reconstruction from limited tomographic data' (Defrise et al 2006 Inverse Problems 22 1037). This continuation tackles new cases of incomplete data that could be of interest in applications of computed tomography.