Discrete non-abelian X-ray transforms

2025/09/04 by Gupta, Pranav, Novikov, Roman
#44A12 #65N21 #65N22 #65R10 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2510.09611

Abstract

We define a discrete version of the non-abelian X-ray transform, going back in particular to Manakov, Zakharov (1981) and Strichartz (1982). We extend to this transform non-overdetermined reconstruction results obtained for the abelian case in the recent article by Novikov, Sharma (2025). In addition, we establish relations with the continuous non-abelian X-ray transform. In this respect, our results include an explicit and exact non-overdetermined layer-stripping reconstruction procedure for piecewise constant matrix-valued functions from their continuous non-abelian X-ray transform. To our knowledge, this result is new even for the classical X-ray transform.

Citations

• On discrete X-ray transform
• Consistent Inversion of Noisy Non-Abelian X-Ray Transforms
• A breakdown of injectivity for weighted ray transforms in\n multidimensions

Related

• On discrete X-ray transform
• Stability of the non-abelian X-ray transform in dimension ≥ 3
• The non-Abelian X-ray transform on surfaces
• Computerized Tomography and Reproducing Kernels
• Consistent Inversion of Noisy Non-Abelian X-Ray Transforms