Stability estimate for the broken non-abelian x-ray transform in Minkowski space. (1st October 2022)

• Record Type: Journal Article
• Authors: St-Amant, Simon
• Is Part Of: Inverse problems. Volume 38:Number 10(2022)
• Publication Date: 2022-10-01
• Subjects: non-abelian x-ray transform -- stability estimate -- inverse problem for Yang–Mills equations -- broken ray transform -- gauge -- light-sink connection -- Bayesian inverse problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac88f2
• Languages: English
• ISSNs: 0266-5611

Abstract

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 the gauge into account, 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.