An explicit reconstruction algorithm for the transverse ray transform of a second rank tensor field from three axis data. (28th September 2016)

• Record Type: Journal Article
• Authors: Desai, Naeem M; Lionheart, William R B
• Is Part Of: Inverse problems. Volume 32:Number 11(2016:Nov.)
• Publication Date: 2016-09-28
• Subjects: tensor tomography -- transverse ray transform -- diffraction tomography -- strain; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/11/115009
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We give an explicit plane-by-plane filtered back-projection reconstruction algorithm for the transverse ray transform of symmetric second rank tensor fields on Euclidean three-space, using data from rotation about three orthogonal axes. We show that in the general case two-axis data is insufficient, but we give an explicit reconstruction procedure for the potential case with two-axis data. We describe a numerical implementation of the three-axis algorithm and give reconstruction results for simulated data.