Eleven Primitives and Three Gates: The Universal Structure of Computational Imaging
This provides a foundational grammar for designing and diagnosing computational imaging systems across all modalities, addressing a broad problem for researchers and engineers in imaging.
The paper tackles the problem of diverse computational imaging systems lacking a unified design and diagnosis framework, proving that all such systems decompose into 11 primitives and three root causes of failure, with validation showing recovery improvements of +0.8 to +13.9 dB on deployed instruments.
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.