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Non-abelian  X -ray tomography seeks to recover a matrix potential    $$\Phi :M\rightarrow {\mathbb {C}}^{m\times m}$$  Φ : M → C m × m in a domain  M  from measurements of its so-called scattering data    $$C_\Phi $$  C Φ at    $$\partial M$$  ∂ M . For    $$\dim M\ge 3$$  dim M ≥ 3 (and under appropriate convexity and regularity conditions), injectivity of the forward map    $$\Phi \mapsto C_\Phi $$  Φ ↦ C Φ was established in (Paternain et al. in Am J Math 141(6):1707–1750, 2019). The present article extends this result by proving a Hölder-type stability estimate. As an application, a statistical consistency result for    $$\dim M =2$$  dim M = 2 (Monard et al. in Commun Pure Appl Math, 2019) is generalised to higher dimensions. The injectivity proof in (Paternain et al. in Am J Math 141(6):1707–1750, 2019) relies on a novel method by Uhlmann and Vasy (Invent Math 205(1):83–120, 2016), which first establishes injectivity in a shallow layer below    $$\partial M$$  ∂ M and then globalises this by a layer stripping argument. The main technical contribution of this paper is a more quantitative version of these arguments, in particular, proving uniform bounds on layer depth and stability constants.

Stability of the Non-abelian X-ray Transform in Dimension $$\ge 3$$