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arXiv · 2603.18728

Reconstructions of Single Pixel X-Ray Transforms with Applications in Nuclear-Disarmament Verification

Christopher Fichtlscherer·R. Scott Kemp·Christina Brandt
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Abstract

In nuclear arms control and disarmament processes, it is crucial to determine whether an object is a nuclear weapon or not without revealing sensitive information about it. At the MIT: Laboratory for Nuclear Security and Policy, such a nuclear verification method was developed, showcasing a transmission-based approach [1]. This method's essential part rests on a mathematical operation, the Single-Pixel X-Ray Transform: a cone of X-rays transmits an object and the remaining intensity is measured with a single-pixel detector. This transformation and the recovery of objects from dimensionless single-pixel measurements more generally has only been analyzed to a limited extent. In this work, we investigate some of the Single Pixel X-Ray Transform's mathematical properties. More specifically, we show that the Single Pixel X-ray transform is non-linear, continuous, Fréchet-differentiable and convex. We also introduce a method of reconstructing an object based only on a finite number of dimensionless, noisy Single Pixel X-Ray Transform measurement values. This method is based on Douglas-Rachford splitting and uses total variation denoising. We present an implementation for this method, focusing on rotational symmetric objects, as they allow the use of a one-dimensional direct total variation denoising algorithm [2].

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Christopher Fichtlscherer, R. Scott Kemp, Christina Brandt. 2026-03-19. Reconstructions of Single Pixel X-Ray Transforms with Applications in Nuclear-Disarmament Verification. https://arxiv.org/abs/2603.18728

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