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

TL;DR

This paper reveals a universal structural framework for computational imaging systems, decomposing them into 11 primitives and 3 gates, enabling systematic design, diagnosis, and correction across diverse modalities.

Contribution

It introduces a minimal primitive basis and triad decomposition that unify the understanding and improvement of computational imaging systems.

Findings

Validated across 12 modalities and 5 carrier families.

Achieved +0.8 to +13.9 dB recovery on deployed instruments.

Established a universal grammar for computational imaging design and diagnosis.

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.