Differentiable Imaging
From resilient to co-designed computational imaging

Wikipedia


1King Abdullah University of Science and Technology

2University of Arizona

3Tsinghua University

4Virginia Tech

5Seoul National University

6The University of Hong Kong

1The University of Hong Kong

2University of Arizona

Abstract

Differentiable Imaging is a framework that seamlessly integrates optical hardware with computational algorithms to address critical challenges in traditional computational imaging. By leveraging differentiable programming, this approach enables end-to-end optimization of the whole imaging systems while accounting for real-world physical imperfections. The differentiable imaging framework leads to simplified hardware designs, enhanced imaging performance, and resilience imaging across diverse imaging modalities. The differentiable linkage among all system components ultimately enables genuine co-design in computational imaging.

Introduction

Sources of uncertainty in computational imaging systems
Typical Uncertainties that lead to mismatch.

Computational imaging has made significant advances but continues to face substantial challenges from system uncertainties. These uncertainties can be categorized into five key areas:

Effective co-design requires multi-variable optimization with accurate mathematical modeling of real systems. These uncertainties not only hinder precise numerical modeling but also complicate inverse problem solving, creating a fundamental bottleneck in computational imaging advancement.

Technical Framework

Differentiable imaging framework
Comparison of Computational Imaging and Differentiable Imaging.

Differentiable imaging 1 fundamentally redefines co-design by integrating physically accurate models within machine learning architectures for comprehensive end-to-end optimization. This framework specifically targets uncertainties that cause critical mismatches between real-world systems and their numerical representations. Through differentiable programming and automatic differentiation, these uncertainties are explicitly modeled and their impacts systematically mitigated.

By leveraging differentiable programming, differentiable imaging offers an elegant solution to the limitations of conventional computational imaging. Rather than pursuing increasingly complex yet cumbersome physical models, differentiable imaging fundamentally reconceptualizes the imaging process. It transforms the traditional encoding model $y=f(x)$ into a more comprehensive formulation $y=f(x, \theta)$, where $\theta$ represents a parameter set specifically designed to address and compensate for mismatches between physical systems and numerical models.

The complete forward model captures the entire imaging pipeline through a series of interconnected transformations:

\[\begin{equation} y = f(x, \theta), \qquad f = f_{noise} \circ f_c \circ f_{oc} \circ f_x \circ f_{oi} \circ f_i, \end{equation}\]

where the function composition operator $\circ$ connects each system component, and $\theta = { \theta_c, \theta_{oc}, \ldots }$ encompasses all system parameters. Each component corresponds to specific physical processes within the imaging system, from illumination characteristics through object interactions to sensor behavior and noise sources.

This comprehensive forward model enables the formulation of an elegant inverse problem that simultaneously optimizes system parameters while reconstructing images:

\[\begin{equation} x^*, \theta^* = \text{argmin}_{x, \theta} \mathcal{L}(f(x, \theta), y) + \sum_{n=1}^N \beta_n \mathcal{R}_n(x) \\ s.t. \quad x \in \Omega_x, \theta \in \Omega_{\theta} \end{equation}\]

Here, $\mathcal{L}(f(x, \theta), y)$ represents the fidelity term that quantifies the discrepancy between the model predictions and measured data. While the ${\ell_2}$ loss $\mathcal{L}(f(x, \theta), y) = |f(x, \theta) - y|^2$ is commonly used due to its mathematical tractability and compatibility with Gaussian noise assumptions, the selection of an appropriate fidelity function depends critically on the specific imaging conditions and noise characteristics.

The framework introduces two primary innovations:

  1. System Imperfection Modeling: Direct integration of hardware imperfections into imaging models (represented as $f(x,\theta)$ where $\theta$ encapsulates uncertainty parameters)
  2. Differentiable Optimization: Implementation of inverse problem solving using differentiable optimization algorithms, enabling gradient-based optimization across the entire imaging pipeline

This integrated methodology facilitates closed-loop optimization, resulting in robust, high-performance imaging systems that maintain effectiveness despite real-world imperfections.

Research Achievements

Since 2021, our exploration of differentiable imaging across various domains has led to significant advancements:

Techniques Uncertainties Achievements
Differentiable Holography2,3 Defocus distance; Complex light-wave interaction; Single-shot wavefield imaging; high-density Single-shot 3D PIV
Differentiable Lensless Imaging4 Sensor scanning positions; defocus distances; Pixel-super resolution; High-performance imaging; Compact and cost-effective hardware
Uncertainty-Aware Fourier Ptychography5 Modelable: misalignment, element aberrations;
Statistical: noise, low quality data
Simplified measurements; resolution beyond traditional physical limits; expanded system functions

Our research has revealed three fundamental principles:

  1. Precision in Modeling: The accuracy of optical system modeling is paramount to successful implementation
  2. Physics-Grounded Algorithms: Algorithms rooted in fundamental physical principles ensure computational efficiency, system robustness, and result interpretability
  3. System-Algorithm Synergy: Effective interplay between physical hardware and computational models is crucial for both imaging quality and optimal system design

Powered by differentiable programming, differentiable imaging has emerged as a pivotal force in computational imagingβ€”its significance far transcends uncertainty-aware computation. Acting as a unifying nexus, it enables seamless integration across the core components of computational imaging: it harmonizes hardware design with software reconstruction, ensuring a fluid transition from physical devices to algorithmic implementations; it connects numerical optimization and machine learning, fueling continuous advancements in algorithm performance; it bridges mathematical theory, information theory, and physical realization, translating abstract concepts into practical, high-impact technical solutions; and it drives deep integration across optics, material science, and computational sciences, dismantling long-entrenched disciplinary silos. Through this interconnected framework, all components mutually reinforce and co-evolve, ultimately realizing the long-pursued goal of global optimization in computational imaging.

Digital Twin equipped Computational Imaging
Digital Twin equipped Computational Imaging.

The potential of differentiable imaging extends well beyond its current applications. Future advancements may include integration with digital twin technology and contributions to AI for Science initiatives 6, thereby unlocking new paradigms for scientific discovery and technological innovation.

  1. Ni Chen, Liangcai Cao, Ting-Chung Poon, Byoungho Lee, Edmund Y. Lam, β€œDifferentiable Imaging: A New Tool for Computational Optical Imaging,” Advanced Physics Research, 2023.Β 

  2. Ni Chen, Congli Wang, Wolfgang Heidrich, β€œβˆ‚H: Differentiable Holography,” Laser & Photonics Reviews, 2023.Β 

  3. Yang Wu, Jun Wang, Sigurdur Thoroddsen, Ni Chen*, β€œSingle-Shot High-Density Volumetric Particle Imaging Enabled by Differentiable Holography,” IEEE Transactions on Industrial Informatics, 2024.Β 

  4. Ni Chen, Edmund Y. Lam, β€œDifferentiable pixel-super-resolution lensless imaging,” Optics Letters, 2025.Β 

  5. Ni Chen, Yang Wu, Chao Tan, Liangcai Cao, Jun Wang, Edmund Y. Lam, β€œUncertainty-Aware Fourier Ptychography,” Light: Science & Applications, 2025.Β 

  6. Ni Chen, David J. Brady, Edmund Y. Lam, β€œDifferentiable Imaging: progress, challenges, and outlook,” Advanced Devices & Instrumentation, 2025.Β