PDE-based numerical method for a limited angle x-ray tomography. (21st March 2019)

• Record Type: Journal Article
• Authors: Klibanov, Micheal V; Nguyen, Loc H
• Is Part Of: Inverse problems. Volume 35:Number 4(2019)
• Publication Date: 2019-03-21
• Subjects: tomographic inverse problem -- x-ray transform -- incomplete data -- Carleman estimate; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab0133
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: A new numerical method for x-ray tomography for a specific case of incomplete Radon data is proposed. Potential applications are in checking out bulky luggage in airports. This method is based on the analysis of the transport PDE governing the x-ray tomography rather than on the conventional integral formulation. The quasi-reversibility method is applied. Convergence analysis is performed using a new Carleman estimate. Numerical results are presented and compared with the inversion of the Radon transform using the well-known filtered back projection algorithm. In addition, it is shown how to use our method to study the inversion of the attenuated x-ray transform for the same case of incomplete data.