Draft:Differentiable Imaging

Differentiable imaging is a transformative paradigm in computational imaging. It integrates physical system modeling with computational optimization, enabling end-to-end optimization of integrated optical - computational systems.

At its core, differentiable imaging redefines the imaging process. It transforms the traditional encoding model y=f(x) into y=f(x,θ), where θ is a set of parameters designed to address and compensate for the mismatches between physical systems and numerical models. This comprehensive forward model captures the entire imaging pipeline through a series of interconnected transformations.

One of the key features of differentiable imaging is its ability to handle uncertainties. It can systematically manage both deterministic uncertainties, such as manufacturing tolerances, alignment errors, and optical aberrations, and stochastic uncertainties, including sensor noise, light source fluctuations, and environmental variations. By incorporating explicit numerical models for deterministic variations and leveraging differentiable optimization frameworks for stochastic fluctuations, it improves the robustness of imaging systems in real - world applications.

Differentiable imaging also enables true system co - design. It allows for the simultaneous optimization of optical and computational elements as an integrated system, rather than separate entities. This has led to significant breakthroughs in areas like Point Spread Function (PSF) engineering, microscope system optimization, and lens design.

In addition, it extends imaging capabilities while compensating for hardware limitations. It can address challenges in non - visible wavelength imaging, such as sub - optimal optical component performance, high costs, and low signal - to - noise ratios. By using computational techniques to compensate for hardware imperfections, it enables high - quality imaging with more practical and cost - effective hardware implementations.