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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.18728 |
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| _version_ | 1866917352941027328 |
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| author | Fichtlscherer, Christopher Kemp, R. Scott Brandt, Christina |
| author_facet | Fichtlscherer, Christopher Kemp, R. Scott Brandt, Christina |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18728 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reconstructions of Single Pixel X-Ray Transforms with Applications in Nuclear-Disarmament Verification Fichtlscherer, Christopher Kemp, R. Scott Brandt, Christina Numerical Analysis 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]. |
| title | Reconstructions of Single Pixel X-Ray Transforms with Applications in Nuclear-Disarmament Verification |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.18728 |