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Statistical aspects of the non-abelian X-ray transform

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RNTW03 - New tomographic methods using particles

I will discuss some recent developments providing theoretical guarantees for Bayesian inversion with Gaussian priors for a class of nonlinear inverse problems.These developments will be illustrated in a specific inverse problem: the non-abelian X-ray transform.This problem underpins new experiments designed to measure magnetic fields inside materials by shooting them with neutron beams from different directions, like in a CT scan.The theoretical guarantees will be of two types: first I will discuss consistency and then uncertainty quantification. This is based on joint work with F. Monard and R. Nickl

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

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