Microlocal inversion of a 3-dimensional restricted transverse ray transform of symmetric m-tensor fields

2019/04/04 by Krishnan, Venkateswaran P., Mishra, Rohit Kumar, Sahoo, Suman Kumar
#35R30 #35S30 #46F12 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary #Secondary

paper · doi:10.48550/arxiv.1904.02812

Abstract

We study the problem of inverting a restricted transverse ray transform to recover a symmetric m-tensor field in ℝ³ using microlocal analysis techniques. More precisely, we prove that a symmetric m-tensor field can be recovered up to a known singular term and a smoothing term if its transverse ray transform is known along all lines intersecting a fixed smooth curve satisfying the Kirillov-Tuy condition.

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