Interior tomography: theory, algorithms and applications

Hengyong Yu; Yangbo Ye; Ge Wang

doi:10.1117/12.794981

15 September 2008 Interior tomography: theory, algorithms and applications

Hengyong Yu, Yangbo Ye, Ge Wang

Proceedings Volume 7078, Developments in X-Ray Tomography VI; 70780F (2008) https://doi.org/10.1117/12.794981
Event: Optical Engineering + Applications, 2008, San Diego, California, United States

Abstract

The conventional wisdom states that the interior problem (reconstruction of an interior region from projection data along lines only through that region) is NOT uniquely solvable. While it remains correct, our recent theoretical and numerical results demonstrated that this interior problem CAN be solved in a theoretically exact and numerically stable fashion if a sub-region within the interior region is known. In contrast to the well-established lambda tomography, the studies on this type of exact interior reconstruction are referred to as "interior tomography". In this paper, we will overview the development of interior tomography, involving theory, algorithms and applications. The essence of interior tomography is to find the unique solution from highly truncated projection data via analytic continuation. Such an extension can be done either in the filtered backprojection or backprojection filtration formats. The key issue for the exact interior reconstruction is how to invert the truncated Hilbert transform. We have developed a projection onto convex set (POCS) algorithm and a singular value decomposition (SVD) method and produced excellent results in numerical simulations and practical applications.

Citation Download Citation

Hengyong Yu, Yangbo Ye, and Ge Wang "Interior tomography: theory, algorithms and applications", Proc. SPIE 7078, Developments in X-Ray Tomography VI, 70780F (15 September 2008); https://doi.org/10.1117/12.794981

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