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Explicit inversion formulas for normal operators of momentum ray transforms

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RNTW03 - New tomographic methods using particles

We study certain weighted ray transforms of symmetric tensor fields called momentum ray transforms. In the absence of weights, the ray transform reduces to the standard ray transform of symmetric tensor fields, and full inversion of the ray transform recovering the symmetric tensor field is not possible due to the presence of an infinite dimensional null space. The supplementary data in the form of higher order moments of the ray transform leads to explicit recovery of the entire tensor field. In this talk, instead of the momentum ray transforms, we will focus our attention on normal operators associated to momentum ray transforms (the composition of the transform with its formal adjoint), and introduce an approach for the explicit reconstruction of the entire symmetric tensor field from this data.

This talk is part of the Isaac Newton Institute Seminar Series series.

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