Stability estimate for the broken non-abelian X-ray transform in Minkowski space

TL;DR

This paper establishes a stability estimate for the broken non-abelian X-ray transform in Minkowski space, providing a new proof of injectivity and demonstrating the recovery of certain connections from noisy data via Bayesian inversion.

Contribution

It introduces a stability estimate accounting for gauge invariance and develops a method to recover light-sink connections from noisy measurements.

Findings

Proves a stability estimate for the non-abelian X-ray transform.

Provides a new proof of the transform's injectivity.

Demonstrates Bayesian inversion for recovering light-sink connections.

Abstract

We study the broken non-abelian X-ray transform in Minkowski space. This transform acts on the space of Hermitian connections on a causal diamond and is known to be injective up to an infinite-dimensional gauge. We show a stability estimate that takes into account the gauge, leading to a new proof of the transform's injectivity. Our proof leads us to consider a special type of connections that we call light-sink connections. We then show that we can consistently recover a light-sink connection from noisy measurement of its X-ray transform data through Bayesian inversion.