Modern nanofabrication techniques have enabled us to manipulate the wave-front of light with sub-wavelength-scale structures, offering the potential to replace bulky refractive surfaces in conventional optics with ultrathin metasurfaces. In theory, arrays of nanoposts provide unprecedented control over manipulating the wavefront in terms of phase, polarization, and amplitude at the nanometer resolution. A line of recent work successfully investigates flat computational cameras that replace compound lenses with a single metalens or an array of metasurfaces a few millimeters from the sensor. However, due to the inherent wavelength dependence of metalenses, in practice, these cameras do not match their refractive counterparts in image quality for broadband imaging, and may even suffer from hallucinations when relying on generative reconstruction methods. In this work, we investigate a collaborative array of metasurface elements that are jointly learned to perform broadband imaging. To this end, we learn a nanophotonics array with 100-million nanoposts that is end-to-end jointly optimized over the full visible spectrum—a design task that existing inverse design methods or learning approaches cannot support due to memory and compute limitations. We introduce a distributed meta-optics learning method to tackle this challenge. This allows us to optimize a large parameter array along with a learned metaatom proxy and a non-generative reconstruction method that is parallax-aware and noise-aware. The proposed camera performs favorably in simulation and in all experimental tests irrespective of the scene illumination spectrum.

Differentiable optics, as an emerging paradigm that jointly optimizes optics and (optional) image processing algorithms, has made many innovative optical designs possible across a broad range of imaging and display applications. Many of these systems utilize diffractive optical components for holography, PSF engineering, or wavefront shaping. Existing approaches have, however, mostly remained limited to laboratory prototypes, owing to a large quality gap between simulation and manufactured devices. We aim at lifting the fundamental technical barriers to the practical use of learned diffractive optical systems. To this end, we propose a fabrication-aware design pipeline for diffractive optics fabricated by direct-write grayscale lithography followed by replication with nano-imprinting, which is directly suited for inexpensive mass-production of large area designs. We propose a super-resolved neural lithography model that can accurately predict the 3D geometry generated by the fabrication process. This model can be seamlessly integrated into existing differentiable optics frameworks, enabling fabrication-aware, end-to-end optimization of computational optical systems. To tackle the computational challenges, we also devise tensor-parallel compute framework centered on distributing large-scale FFT computation across many GPUs. As such, we demonstrate large scale diffractive optics designs up to 32.16 mm × 21.44 mm, simulated on grids of up to 128,640 by 85,760 feature points. We find adequate agreement between simulation and fabricated prototypes for applications such as holography and PSF engineering. We also achieve high image quality from an imaging system comprised only of a single diffractive optical element, with images processed only by a one-step inverse filter utilizing the simulation PSF. We believe our findings lift the fabrication limitations for real-world applications of diffractive optics and differentiable optical design.

Tasks across diverse application domains can be posed as large-scale optimization problems, these include graphics, vision, machine learning, imaging, health, scheduling, planning, and energy system forecasting. Independently of the application domain, proximal algorithms have emerged as a formal optimization method that successfully solves a wide array of existing problems, often exploiting problem-specific structures in the optimization. Although model-based formal optimization provides a principled approach to problem modeling with convergence guarantees, at first glance, this seems to be at odds with black-box deep learning methods. A recent line of work shows that, when combined with learning-based ingredients, model-based optimization methods are effective, interpretable, and allow for generalization to a wide spectrum of applications with little or no extra training data. However, experimenting with such hybrid approaches for different tasks by hand requires domain expertise in both proximal optimization and deep learning, which is often error-prone and time-consuming. Moreover, naively unrolling these iterative methods produces lengthy compute graphs, which when differentiated via autograd techniques results in exploding memory consumption, making batch-based training challenging. In this work, we introduce ∇-Prox, a domain-specific modeling language and compiler for large-scale optimization problems using differentiable proximal algorithms. ∇-Prox allows users to specify optimization objective functions of unknowns concisely at a high level, and intelligently compiles the problem into compute and memory-efficient differentiable solvers. One of the core features of ∇-Prox is its full differentiability, which supports hybrid model- and learning-based solvers integrating proximal optimization with neural network pipelines. Example applications of this methodology include learning-based priors and/or sample-dependent inner-loop optimization schedulers, learned with deep equilibrium learning or deep reinforcement learning. With a few lines of code, we show ∇-Prox can generate performant solvers for a range of image optimization problems, including end-to-end computational optics, image deraining, and compressive magnetic resonance imaging. We also demonstrate ∇-Prox can be used in a completely orthogonal application domain of energy system planning, an essential task in the energy crisis and the clean energy transition, where it outperforms state-of-the-art CVXPY and commercial Gurobi solvers.

Plug-and-Play (PnP) is a non-convex optimization framework that combines proximal algorithms, for example, the alternating direction method of multipliers (ADMM), with advanced denoising priors. Over the past few years, great empirical success has been obtained by PnP algorithms, especially for the ones that integrate deep learning-based denoisers. However, a key problem of PnP approaches is the need for manual parameter tweaking which is essential to obtain high-quality results across the high discrepancy in imaging conditions and varying scene content. In this work, we present a class of tuning-free PnP proximal algorithms that can determine parameters such as denoising strength, termination time, and other optimization-specific parameters automatically. A core part of our approach is a policy network for automated parameter search which can be effectively learned via a mixture of model-free and model-based deep reinforcement learning strategies. We demonstrate, through rigorous numerical and visual experiments, that the learned policy can customize parameters to different settings, and is often more efficient and effective than existing handcrafted criteria. Moreover, we discuss several practical considerations of PnP denoisers, which together with our learned policy yield state-of-the-art results. This advanced performance is prevalent on both linear and nonlinear exemplar inverse imaging problems, and in particular shows promising results on compressed sensing MRI, sparse-view CT, single-photon imaging, and phase retrieval.

Enhancing the visibility in extreme low-light environments is a challenging task. Under nearly lightless condition, existing image denoising methods could easily break down due to significantly low SNR. In this paper, we systematically study the noise statistics in the imaging pipeline of CMOS photosensors, and formulate a comprehensive noise model that can accurately characterize the real noise structures. Our novel model considers the noise sources caused by digital camera electronics which are largely overlooked by existing methods yet have significant influence on raw measurement in the dark. It provides a way to decouple the intricate noise structure into different statistical distributions with physical interpretations. Moreover, our noise model can be used to synthesize realistic training data for learning-based low-light denoising algorithms. In this regard, although promising results have been shown recently with deep convolutional neural networks, the success heavily depends on abundant noisy-clean image pairs for training, which are tremendously difficult to obtain in practice. Generalizing their trained models to images from new devices is also problematic. Extensive experiments on multiple low-light denoising datasets - including a newly collected one in this work covering various devices - show that a deep neural network trained with our proposed noise formation model can reach surprisingly-high accuracy. The results are on par with or sometimes even outperform training with paired real data, opening a new door to real-world extreme low-light photography.

In this article, we propose an alternating directional 3-D quasi-recurrent neural network for hyperspectral image (HSI) denoising, which can effectively embed the domain knowledge-structural spatiospectral correlation and global correlation along spectrum (GCS). Specifically, 3-D convolution is utilized to extract structural spatiospectral correlation in an HSI, while a quasi-recurrent pooling function is employed to capture the GCS. Moreover, the alternating directional structure is introduced to eliminate the causal dependence with no additional computation cost. The proposed model is capable of modeling spatiospectral dependence while preserving the flexibility toward HSIs with an arbitrary number of bands. Extensive experiments on HSI denoising demonstrate significant improvement over the state-of-the-art under various noise settings, in terms of both restoration accuracy and computation time. Our code is available at https://github.com/Vandermode/QRNN3D.

Lacking rich and realistic data, learned single image denoising algorithms generalize poorly in real raw images that not resemble the data used for training. Although the problem can be alleviated by the heteroscedastic Gaussian noise model, the noise sources caused by digital camera electronics are still largely overlooked, despite their significant effect on raw measurement, especially under extremely low-light condition. To address this issue, we present a highly accurate noise formation model based on the characteristics of CMOS photosensors, thereby enabling us to synthesize realistic samples that better match the physics of image formation process. Given the proposed noise model, we additionally propose a method to calibrate the noise parameters for available modern digital cameras, which is simple and reproducible for any new device. We systematically study the generalizability of a neural network trained with existing schemes, by introducing a new low-light denoising dataset that covers many modern digital cameras from diverse brands. Extensive empirical results collectively show that by utilizing our proposed noise formation model, a network can reach the capability as if it had been trained with rich real data, which demonstrates the effectiveness of our noise formation model.

Plug-and-play (PnP) is a non-convex framework that combines ADMM or other proximal algorithms with advanced denoiser priors. Recently, PnP has achieved great empirical success, especially with the integration of deep learning-based denoisers. However, a key problem of PnP based approaches is that they require manual parameter tweaking. It is necessary to obtain high-quality results across the high discrepancy in terms of imaging conditions and varying scene content. In this work, we present a tuning-free PnP proximal algorithm, which can automatically determine the internal parameters including the penalty parameter, the denoising strength and the terminal time. A key part of our approach is to develop a policy network for automatic search of parameters, which can be effectively learned via mixed model-free and model-based deep reinforcement learning. We demonstrate, through numerical and visual experiments, that the learned policy can customize different parameters for different states, and often more efficient and effective than existing handcrafted criteria. Moreover, we discuss the practical considerations of the plugged denoisers, which together with our learned policy yield state-of-the-art results. This is prevalent on both linear and nonlinear exemplary inverse imaging problems, and in particular, we show promising results on Compressed Sensing MRI and phase retrieval.

Removing undesirable reflections from a single image captured through a glass window is of practical importance to visual computing systems. Although state-of-the-art methods can obtain decent results in certain situations, performance declines significantly when tackling more general real-world cases. These failures stem from the intrinsic difficulty of single image reflection removal -- the fundamental ill-posedness of the problem, and the insufficiency of densely-labeled training data needed for resolving this ambiguity within learning-based neural network pipelines. In this paper, we address these issues by exploiting targeted network enhancements and the novel use of misaligned data. For the former, we augment a baseline network architecture by embedding context encoding modules that are capable of leveraging high-level contextual clues to reduce indeterminacy within areas containing strong reflections. For the latter, we introduce an alignment-invariant loss function that facilitates exploiting misaligned real-world training data that is much easier to collect. Experimental results collectively show that our method outperforms the state-of-the-art with aligned data, and that significant improvements are possible when using additional misaligned data.