Eleven Primitives and Three Gates: The Universal Structure of Computational Imaging

• URL: http://arxiv.org/abs/2603.13521v1
• Date: Fri, 13 Mar 2026 18:54:35 GMT
• Title: Eleven Primitives and Three Gates: The Universal Structure of Computational Imaging
• Abstract summary: We prove that every imaging forward model decomposes into a directed acyclic graph over exactly 11 physically typed primitives.<n>We prove that every reconstruction failure has exactly three independent root causes: information deficiency, carrier noise, and operator mismatch.
• Score: 8.513179174301722
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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