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

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