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

arXiv: https://arxiv.org/abs/2603.13521 · HTML: https://mlsanity.com/paper/2603.13521/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 53 references that are in the map.
- First posted on arXiv 13 Mar 2026.

## Builds on (most cited first, 11 of 11)

- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Mask-guided Spectral-wise Transformer for Efficient Hyperspectral Image Reconstruction](https://mlsanity.com/paper/2111.07910/) (2021)
- [HDNet: High-resolution Dual-domain Learning for Spectral Compressive Imaging](https://mlsanity.com/paper/2203.02149/) (2022)
- [Deep Gaussian Scale Mixture Prior for Spectral Compressive Imaging](https://mlsanity.com/paper/2103.07152/) (2021)
- [Coded aperture compressive temporal imaging](https://mlsanity.com/paper/1302.2575/) (2013)
- [DiffuserCam: Lensless Single-exposure 3D Imaging](https://mlsanity.com/paper/1710.02134/) (2017)
- [Plug-and-Play Algorithms for Video Snapshot Compressive Imaging](https://mlsanity.com/paper/2101.04822/) (2021)
- [EfficientSCI: Densely Connected Network with Space-time Factorization for Large-scale Video Snapshot Compressive Imaging](https://mlsanity.com/paper/2305.10006/) (2023)
- [Intelligent Parameter Tuning in Optimization-based Iterative CT Reconstruction via Deep Reinforcement Learning](https://mlsanity.com/paper/1711.00414/) (2017)
- [The Finite Primitive Basis Theorem for Computational Imaging: Formal Foundations of the OperatorGraph Representation](https://mlsanity.com/paper/2602.20550/) (2026)

## Built on by (most cited first, 1 of 1)

- [Designing Any Imaging System from Natural Language: Agent-Constrained Composition over a Finite Primitive Basis](https://mlsanity.com/paper/2603.25636/) (2026)

## Abstract (arXiv)

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.