Eleven Primitives and Three Gates: The Universal Structure of Computational Imaging
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911514681671680 |
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| author | Yang, Chengshuai Yuan, Xin |
| author_facet | Yang, Chengshuai Yuan, Xin |
| contents | Computational imaging systems -- from coded-aperture cameras to cryo-electron microscopes -- span five carrier families yet share a hidden structural simplicity. We prove that every imaging forward model decomposes into a directed acyclic graph over exactly 11 physically typed primitives (Finite Primitive Basis Theorem) -- a sufficient and minimal basis that provides a compositional language for designing any imaging modality. We further prove that every reconstruction failure has exactly three independent root causes: information deficiency, carrier noise, and operator mismatch (Triad
Decomposition). The three gates map to the system lifecycle: Gates 1 and 2 guide design (sampling geometry, carrier
selection); Gate 3 governs deployment-stage calibration and drift correction. Validation across 12 modalities and all
five carrier families confirms both results, with +0.8 to +13.9 dB recovery on deployed instruments. Together, the 11
primitives and 3 gates establish the first universal grammar for designing, diagnosing, and correcting computational
imaging systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13521 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eleven Primitives and Three Gates: The Universal Structure of Computational Imaging Yang, Chengshuai Yuan, Xin Computer Vision and Pattern Recognition 68U10, 94A08 I.4.5; I.4.9 Computational imaging systems -- from coded-aperture cameras to cryo-electron microscopes -- span five carrier families yet share a hidden structural simplicity. We prove that every imaging forward model decomposes into a directed acyclic graph over exactly 11 physically typed primitives (Finite Primitive Basis Theorem) -- a sufficient and minimal basis that provides a compositional language for designing any imaging modality. We further prove that every reconstruction failure has exactly three independent root causes: information deficiency, carrier noise, and operator mismatch (Triad Decomposition). The three gates map to the system lifecycle: Gates 1 and 2 guide design (sampling geometry, carrier selection); Gate 3 governs deployment-stage calibration and drift correction. Validation across 12 modalities and all five carrier families confirms both results, with +0.8 to +13.9 dB recovery on deployed instruments. Together, the 11 primitives and 3 gates establish the first universal grammar for designing, diagnosing, and correcting computational imaging systems. |
| title | Eleven Primitives and Three Gates: The Universal Structure of Computational Imaging |
| topic | Computer Vision and Pattern Recognition 68U10, 94A08 I.4.5; I.4.9 |
| url | https://arxiv.org/abs/2603.13521 |