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

2026-03-13

AI Summary

This work addresses the absence of a unified theoretical framework in computational imaging systems, which hinders effective diagnosis and optimization of reconstruction failures. The authors propose a universal grammar that decomposes any imaging forward model into a directed acyclic graph composed of eleven fundamental physical primitives. Building upon three root causes—information loss, carrier noise, and operator mismatch—they establish a tripartite decomposition theorem and a corresponding lifecycle gating mechanism to guide system design and calibration. Through graph-theoretic and information-theoretic structural decomposition, formal analysis of forward models, and cross-modal validation, the framework’s completeness and minimality are demonstrated across twelve imaging modalities spanning five carrier families, achieving empirical reconstruction performance gains of 0.8–13.9 dB.

Technology Category

• Computer Vision: Computational Photography, Image & Video Synthesis
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

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.

Problem

• computational imaging
• forward model
• reconstruction failure
• system design
• universal structure

Innovation

• computational imaging
• primitive basis
• forward model decomposition
• reconstruction failure analysis
• universal grammar