Direct integration of the inverse Radon equation for X-ray computed tomography

Article type: Research Article

Authors: Libin, E.E.^a | Chakhlov, S.V.^b | Trinca, D.^{b; *}

Affiliations: [a] Research Institute of Applied Mathematics and Mechanics, Tomsk State University, Russian Federation | [b] Russian-Chinese Laboratory of Radiation Control and Inspection, Tomsk Polytechnic University, Russian Federation

Correspondence: [*] Corresponding author: D. Trinca, Russian-Chinese Laboratory of Radiation Control and Inspection, Tomsk Polytechnic University, Arkadiya Ivanova 8, Tomsk 634028, Russian Federation. Email: [email protected].

Abstract: A new mathematical appoach using the inverse Radon equation for restoration of images in problems of linear two-dimensional x-ray tomography is formulated. In this approach, Fourier transformation is not used, and it gives the chance to create the practical computing algorithms having more reliable mathematical substantiation. Results of software implementation show that for especially for low number of projections, the described approach performs better than standard X-ray tomographic reconstruction algorithms.

Keywords: Optimization, Radon’s inversion equation, tomographic reconstruction, X-ray tomography

DOI: 10.3233/XST-160587

Journal: Journal of X-Ray Science and Technology, vol. 24, no. 6, pp. 787-795, 2016