Christopher A. Metzler

Kevin Zhang, Mingyang Xie, Maharshi Gor et al. · deepmind

Deep image prior (DIP) is a recently proposed technique for solving imaging inverse problems by fitting the reconstructed images to the output of an untrained convolutional neural network. Unlike pretrained feedforward neural networks, the same DIP can generalize to arbitrary inverse problems, from denoising to phase retrieval, while offering competitive performance at each task. The central disadvantage of DIP is that, while feedforward neural networks can reconstruct an image in a single pass, DIP must gradually update its weights over hundreds to thousands of iterations, at a significant computational cost. In this work we use meta-learning to massively accelerate DIP-based reconstructions. By learning a proper initialization for the DIP weights, we demonstrate a 10x improvement in runtimes across a range of inverse imaging tasks. Moreover, we demonstrate that a network trained to quickly reconstruct faces also generalizes to reconstructing natural image patches.

Saurav K. Shastri, Rizwan Ahmad, Christopher A. Metzler et al.

To solve inverse problems, plug-and-play (PnP) methods replace the proximal step in a convex optimization algorithm with a call to an application-specific denoiser, often implemented using a deep neural network (DNN). Although such methods yield accurate solutions, they can be improved. For example, denoisers are usually designed/trained to remove white Gaussian noise, but the denoiser input error in PnP algorithms is usually far from white or Gaussian. Approximate message passing (AMP) methods provide white and Gaussian denoiser input error, but only when the forward operator is sufficiently random. In this work, for Fourier-based forward operators, we propose a PnP algorithm based on generalized expectation-consistent (GEC) approximation -- a close cousin of AMP -- that offers predictable error statistics at each iteration, as well as a new DNN denoiser that leverages those statistics. We apply our approach to magnetic resonance (MR) image recovery and demonstrate its advantages over existing PnP and AMP methods.

Brandon Yushan Feng, Mingyang Xie, Christopher A. Metzler

We present a self-supervised and self-calibrating multi-shot approach to imaging through atmospheric turbulence, called TurbuGAN. Our approach requires no paired training data, adapts itself to the distribution of the turbulence, leverages domain-specific data priors, and can generalize from tens to thousands of measurements. We achieve such functionality through an adversarial sensing framework adapted from CryoGAN, which uses a discriminator network to match the distributions of captured and simulated measurements. Our framework builds on CryoGAN by (1) generalizing the forward measurement model to incorporate physically accurate and computationally efficient models for light propagation through anisoplanatic turbulence, (2) enabling adaptation to slightly misspecified forward models, and (3) leveraging domain-specific prior knowledge using pretrained generative networks, when available. We validate TurbuGAN on both computationally simulated and experimentally captured images distorted with anisoplanatic turbulence.

Matthew A. Chan, Sean I. Young, Christopher A. Metzler

Many imaging inverse problems$\unicode{x2014}$such as image-dependent in-painting and dehazing$\unicode{x2014}$are challenging because their forward models are unknown or depend on unknown latent parameters. While one can solve such problems by training a neural network with vast quantities of paired training data, such paired training data is often unavailable. In this paper, we propose a generalized framework for training image reconstruction networks when paired training data is scarce. In particular, we demonstrate the ability of image denoising algorithms and, by extension, denoising diffusion models to supervise network training in the absence of paired training data.

Sachin Shah, Sakshum Kulshrestha, Christopher A. Metzler

Point-spread-function (PSF) engineering is a powerful computational imaging techniques wherein a custom phase mask is integrated into an optical system to encode additional information into captured images. Used in combination with deep learning, such systems now offer state-of-the-art performance at monocular depth estimation, extended depth-of-field imaging, lensless imaging, and other tasks. Inspired by recent advances in spatial light modulator (SLM) technology, this paper answers a natural question: Can one encode additional information and achieve superior performance by changing a phase mask dynamically over time? We first prove that the set of PSFs described by static phase masks is non-convex and that, as a result, time-averaged PSFs generated by dynamic phase masks are fundamentally more expressive. We then demonstrate, in simulation, that time-averaged dynamic (TiDy) phase masks can offer substantially improved monocular depth estimation and extended depth-of-field imaging performance.

Rushil Joshi, Ethan Adams, Matthew Ziemann et al.

The United States coastline spans 95,471 miles; a distance that cannot be effectively patrolled or secured by manual human effort alone. Unmanned Aerial Vehicles (UAVs) equipped with infrared cameras and deep-learning based algorithms represent a more efficient alternative for identifying and segmenting objects of interest - namely, ships. However, standard approaches to training these algorithms require large-scale datasets of densely labeled infrared maritime images. Such datasets are not publicly available and manually annotating every pixel in a large-scale dataset would have an extreme labor cost. In this work we demonstrate that, in the context of segmenting ships in infrared imagery, weakly-supervising an algorithm with sparsely labeled data can drastically reduce data labeling costs with minimal impact on system performance. We apply weakly-supervised learning to an unlabeled dataset of 7055 infrared images sourced from the Naval Air Warfare Center Aircraft Division (NAWCAD). We find that by sparsely labeling only 32 points per image, weakly-supervised segmentation models can still effectively detect and segment ships, with a Jaccard score of up to 0.756.

Xi Chen, Soham Jana, Christopher A. Metzler et al.

Multilook coherent imaging is a widely used technique in applications such as digital holography, ultrasound imaging, and synthetic aperture radar. A central challenge in these systems is the presence of multiplicative noise, commonly known as speckle, which degrades image quality. Despite the widespread use of coherent imaging systems, their theoretical foundations remain relatively underexplored. In this paper, we study both the theoretical and algorithmic aspects of likelihood-based approaches for multilook coherent imaging, providing a rigorous framework for analysis and method development. Our theoretical contributions include establishing the first theoretical upper bound on the Mean Squared Error (MSE) of the maximum likelihood estimator under the deep image prior hypothesis. Our results capture the dependence of MSE on the number of parameters in the deep image prior, the number of looks, the signal dimension, and the number of measurements per look. On the algorithmic side, we employ projected gradient descent (PGD) as an efficient method for computing the maximum likelihood solution. Furthermore, we introduce two key ideas to enhance the practical performance of PGD. First, we incorporate the Newton-Schulz algorithm to compute matrix inverses within the PGD iterations, significantly reducing computational complexity. Second, we develop a bagging strategy to mitigate projection errors introduced during PGD updates. We demonstrate that combining these techniques with PGD yields state-of-the-art performance. Our code is available at https://github.com/Computational-Imaging-RU/Bagged-DIP-Speckle.

Weiyun Jiang, Haiyun Guo, Christopher A. Metzler et al.

This work introduces the first closed-loop adaptive optics (AO) system capable of optically correcting aberrations in real-time without a guidestar or a wavefront sensor. Nearly 40 years ago, Cederquist et al. demonstrated that asymmetric apertures enable phase retrieval (PR) algorithms to perform fully computational wavefront sensing, albeit at a high computational cost. More recently, Chimitt et al. extended this approach with machine learning and demonstrated real-time wavefront sensing using only a single (guidestar-based) point-spread-function (PSF) measurement. Inspired by these works, we introduce a guidestar-free AO framework built around asymmetric apertures and machine learning. Our approach combines three key elements: (1) an asymmetric aperture placed at the system's pupil plane that enables PR-based wavefront sensing, (2) a pair of machine learning algorithms that estimate the PSF from natural scene measurements and reconstruct phase aberrations, and (3) a spatial light modulator that performs optical correction. We experimentally validate this framework on dense natural scenes imaged through unknown obscurants. Our method outperforms state-of-the-art guidestar-free wavefront shaping methods, using an order of magnitude fewer measurements and three orders of magnitude less computation.

Yu-Hsiang Huang, Levi Burner, Sachin Shah et al.

This work introduces and demonstrates the first system capable of imaging fast-moving extended non-rigid objects through strong atmospheric turbulence at high frame rate. Event cameras are a novel sensing architecture capable of estimating high-speed imagery at thousands of frames per second. However, on their own event cameras are unable to disambiguate scene motion from turbulence. In this work, we overcome this limitation using event-based light field cameras: By simultaneously capturing multiple views of a scene, event-based light field cameras and machine learning-based reconstruction algorithms are able to disambiguate motion-induced dynamics, which produce events that are strongly correlated across views, from turbulence-induced dynamics, which produce events that are weakly correlated across view. Tabletop experiments demonstrate event-based light field can overcome strong turbulence while imaging high-speed objects traveling at up to 16,000 pixels per second.

Christopher A. Metzler, Ali Mousavi, Reinhard Heckel et al.

Learning from unlabeled and noisy data is one of the grand challenges of machine learning. As such, it has seen a flurry of research with new ideas proposed continuously. In this work, we revisit a classical idea: Stein's Unbiased Risk Estimator (SURE). We show that, in the context of image recovery, SURE and its generalizations can be used to train convolutional neural networks (CNNs) for a range of image denoising and recovery problems without any ground truth data. Specifically, our goal is to reconstruct an image $x$ from a noisy linear transformation (measurement) of the image. We consider two scenarios: one where no additional data is available and one where we have measurements of other images that are drawn from the same noisy distribution as $x$, but have no access to the clean images. Such is the case, for instance, in the context of medical imaging, microscopy, and astronomy, where noise-less ground truth data is rarely available. We show that in this situation, SURE can be used to estimate the mean-squared-error loss associated with an estimate of $x$. Using this estimate of the loss, we train networks to perform denoising and compressed sensing recovery. In addition, we also use the SURE framework to partially explain and improve upon an intriguing results presented by Ulyanov et al. in "Deep Image Prior": that a network initialized with random weights and fit to a single noisy image can effectively denoise that image. Public implementations of the networks and methods described in this paper can be found at https://github.com/ricedsp/D-AMP_Toolbox.

Christopher A. Metzler, Philip Schniter, Ashok Veeraraghavan et al.

Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and through scattering media, respectively. Unfortunately, traditional phase retrieval algorithms struggle in the presence of noise. Progress has been made recently on more robust algorithms using signal priors, but at the expense of limiting the range of supported measurement models (e.g., to Gaussian or coded diffraction patterns). In this work we leverage the regularization-by-denoising framework and a convolutional neural network denoiser to create prDeep, a new phase retrieval algorithm that is both robust and broadly applicable. We test and validate prDeep in simulation to demonstrate that it is robust to noise and can handle a variety of system models. A MatConvNet implementation of prDeep is available at https://github.com/ricedsp/prDeep.

Matthew A. Chan, Maria J. Molina, Christopher A. Metzler

Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning to high-stakes applications such as medical imaging and weather forecasting. Conditional diffusion models' breakthrough ability to accurately and efficiently sample from the posterior distribution of a dataset now makes uncertainty estimation conceptually straightforward: One need only train and sample from a large ensemble of diffusion models. Unfortunately, training such an ensemble becomes computationally intractable as the complexity of the model architecture grows. In this work we introduce a new approach to ensembling, hyper-diffusion models (HyperDM), which allows one to accurately estimate both epistemic and aleatoric uncertainty with a single model. Unlike existing single-model uncertainty methods like Monte-Carlo dropout and Bayesian neural networks, HyperDM offers prediction accuracy on par with, and in some cases superior to, multi-model ensembles. Furthermore, our proposed approach scales to modern network architectures such as Attention U-Net and yields more accurate uncertainty estimates compared to existing methods. We validate our method on two distinct real-world tasks: x-ray computed tomography reconstruction and weather temperature forecasting.

Mohamad Qadri, Kevin Zhang, Akshay Hinduja et al.

Underwater perception and 3D surface reconstruction are challenging problems with broad applications in construction, security, marine archaeology, and environmental monitoring. Treacherous operating conditions, fragile surroundings, and limited navigation control often dictate that submersibles restrict their range of motion and, thus, the baseline over which they can capture measurements. In the context of 3D scene reconstruction, it is well-known that smaller baselines make reconstruction more challenging. Our work develops a physics-based multimodal acoustic-optical neural surface reconstruction framework (AONeuS) capable of effectively integrating high-resolution RGB measurements with low-resolution depth-resolved imaging sonar measurements. By fusing these complementary modalities, our framework can reconstruct accurate high-resolution 3D surfaces from measurements captured over heavily-restricted baselines. Through extensive simulations and in-lab experiments, we demonstrate that AONeuS dramatically outperforms recent RGB-only and sonar-only inverse-differentiable-rendering--based surface reconstruction methods. A website visualizing the results of our paper is located at this address: https://aoneus.github.io/

Jingxi Chen, Brandon Y. Feng, Haoming Cai et al.

Video Frame Interpolation aims to recover realistic missing frames between observed frames, generating a high-frame-rate video from a low-frame-rate video. However, without additional guidance, the large motion between frames makes this problem ill-posed. Event-based Video Frame Interpolation (EVFI) addresses this challenge by using sparse, high-temporal-resolution event measurements as motion guidance. This guidance allows EVFI methods to significantly outperform frame-only methods. However, to date, EVFI methods have relied on a limited set of paired event-frame training data, severely limiting their performance and generalization capabilities. In this work, we overcome the limited data challenge by adapting pre-trained video diffusion models trained on internet-scale datasets to EVFI. We experimentally validate our approach on real-world EVFI datasets, including a new one that we introduce. Our method outperforms existing methods and generalizes across cameras far better than existing approaches.

Mingyang Xie, Haiyun Guo, Brandon Y. Feng et al.

Imaging through scattering media is a fundamental and pervasive challenge in fields ranging from medical diagnostics to astronomy. A promising strategy to overcome this challenge is wavefront modulation, which induces measurement diversity during image acquisition. Despite its importance, designing optimal wavefront modulations to image through scattering remains under-explored. This paper introduces a novel learning-based framework to address the gap. Our approach jointly optimizes wavefront modulations and a computationally lightweight feedforward "proxy" reconstruction network. This network is trained to recover scenes obscured by scattering, using measurements that are modified by these modulations. The learned modulations produced by our framework generalize effectively to unseen scattering scenarios and exhibit remarkable versatility. During deployment, the learned modulations can be decoupled from the proxy network to augment other more computationally expensive restoration algorithms. Through extensive experiments, we demonstrate our approach significantly advances the state of the art in imaging through scattering media. Our project webpage is at https://wavemo-2024.github.io/.

Xi Chen, Zhewen Hou, Christopher A. Metzler et al.

We investigate both the theoretical and algorithmic aspects of likelihood-based methods for recovering a complex-valued signal from multiple sets of measurements, referred to as looks, affected by speckle (multiplicative) noise. Our theoretical contributions include establishing the first existing theoretical upper bound on the Mean Squared Error (MSE) of the maximum likelihood estimator under the deep image prior hypothesis. Our theoretical results capture the dependence of MSE upon the number of parameters in the deep image prior, the number of looks, the signal dimension, and the number of measurements per look. On the algorithmic side, we introduce the concept of bagged Deep Image Priors (Bagged-DIP) and integrate them with projected gradient descent. Furthermore, we show how employing Newton-Schulz algorithm for calculating matrix inverses within the iterations of PGD reduces the computational complexity of the algorithm. We will show that this method achieves the state-of-the-art performance.

Tianfu Wang, Mingyang Xie, Haoming Cai et al.

Transparent surfaces, such as glass, create complex reflections that obscure images and challenge downstream computer vision applications. We introduce Flash-Split, a robust framework for separating transmitted and reflected light using a single (potentially misaligned) pair of flash/no-flash images. Our core idea is to perform latent-space reflection separation while leveraging the flash cues. Specifically, Flash-Split consists of two stages. Stage 1 separates apart the reflection latent and transmission latent via a dual-branch diffusion model conditioned on an encoded flash/no-flash latent pair, effectively mitigating the flash/no-flash misalignment issue. Stage 2 restores high-resolution, faithful details to the separated latents, via a cross-latent decoding process conditioned on the original images before separation. By validating Flash-Split on challenging real-world scenes, we demonstrate state-of-the-art reflection separation performance and significantly outperform the baseline methods.

Jiayi Wu, Tianfu Wang, Md Abu Bakr Siddique et al.

Underwater image restoration algorithms seek to restore the color, contrast, and appearance of a scene that is imaged underwater. They are a critical tool in applications ranging from marine ecology and aquaculture to underwater construction and archaeology. While existing pixel-domain diffusion-based image restoration approaches are effective at restoring simple scenes with limited depth variation, they are computationally intensive and often generate unrealistic artifacts when applied to scenes with complex geometry and significant depth variation. In this work we overcome these limitations by combining a novel network architecture (SLURPP) with an accurate synthetic data generation pipeline. SLURPP combines pretrained latent diffusion models -- which encode strong priors on the geometry and depth of scenes -- with an explicit scene decomposition -- which allows one to model and account for the effects of light attenuation and backscattering. To train SLURPP we design a physics-based underwater image synthesis pipeline that applies varied and realistic underwater degradation effects to existing terrestrial image datasets. This approach enables the generation of diverse training data with dense medium/degradation annotations. We evaluate our method extensively on both synthetic and real-world benchmarks and demonstrate state-of-the-art performance. Notably, SLURPP is over 200X faster than existing diffusion-based methods while offering ~ 3 dB improvement in PSNR on synthetic benchmarks. It also offers compelling qualitative improvements on real-world data. Project website https://tianfwang.github.io/slurpp/.

Matthew A. Chan, Casey J. Pellizzari, Christopher A. Metzler

Fourier ptychography (FP) is a powerful light-based synthetic aperture imaging technique that allows one to reconstruct a high-resolution, wide field-of-view image by computationally integrating a diverse collection of low-resolution, far-field measurements. Typically, FP measurement diversity is introduced by changing the angle of the illumination or the position of the camera; either approach results in sampling different portions of the target's spatial frequency content, but both approaches introduce substantial costs and complexity to the acquisition process. In this work, we introduce Inverse Synthetic Aperture Fourier Ptychography, a novel approach to FP that foregoes changing the illumination angle or camera position and instead generates measurement diversity through target motion. Critically, we also introduce a novel learning-based method for estimating k-space coordinates from dual plane intensity measurements, thereby enabling synthetic aperture imaging without knowing the rotation of the target. We experimentally validate our method in simulation and on a tabletop optical system.

Tianxiang Lin, Mohamad Qadri, Kevin Zhang et al.

We consider the problem of optimizing neural implicit surfaces for 3D reconstruction using acoustic images collected with drifting sensor poses. The accuracy of current state-of-the-art 3D acoustic modeling algorithms is highly dependent on accurate pose estimation; small errors in sensor pose can lead to severe reconstruction artifacts. In this paper, we propose an algorithm that jointly optimizes the neural scene representation and sonar poses. Our algorithm does so by parameterizing the 6DoF poses as learnable parameters and backpropagating gradients through the neural renderer and implicit representation. We validated our algorithm on both real and simulated datasets. It produces high-fidelity 3D reconstructions even under significant pose drift.

Tianyi Xiong, Jiayi Wu, Botao He et al.

By combining differentiable rendering with explicit point-based scene representations, 3D Gaussian Splatting (3DGS) has demonstrated breakthrough 3D reconstruction capabilities. However, to date 3DGS has had limited impact on robotics, where high-speed egomotion is pervasive: Egomotion introduces motion blur and leads to artifacts in existing frame-based 3DGS reconstruction methods. To address this challenge, we introduce Event3DGS, an {\em event-based} 3DGS framework. By exploiting the exceptional temporal resolution of event cameras, Event3GDS can reconstruct high-fidelity 3D structure and appearance under high-speed egomotion. Extensive experiments on multiple synthetic and real-world datasets demonstrate the superiority of Event3DGS compared with existing event-based dense 3D scene reconstruction frameworks; Event3DGS substantially improves reconstruction quality (+3dB) while reducing computational costs by 95\%. Our framework also allows one to incorporate a few motion-blurred frame-based measurements into the reconstruction process to further improve appearance fidelity without loss of structural accuracy.

Matthew R. Ziemann, Christopher A. Metzler

We propose a learning-based method for adaptively generating low probability of detection (LPD) radar waveforms that blend into their operating environment. Our waveforms are designed to follow a distribution that is indistinguishable from the ambient radio frequency (RF) background -- while still being effective at ranging and sensing. To do so, we use an unsupervised, adversarial learning framework; our generator network produces waveforms designed to confuse a critic network, which is optimized to differentiate generated waveforms from the background. To ensure our generated waveforms are still effective for sensing, we introduce and minimize an ambiguity function-based loss on the generated waveforms. We evaluate the performance of our method by comparing the single-pulse detectability of our generated waveforms with traditional LPD waveforms using a separately trained detection neural network. We find that our method can generate LPD waveforms that reduce detectability by up to 90% while simultaneously offering improved ambiguity function (sensing) characteristics. Our framework also provides a mechanism to trade-off detectability and sensing performance.

Sean I. Young, Adrian V. Dalca, Enzo Ferrante et al.

Learning-based image reconstruction models, such as those based on the U-Net, require a large set of labeled images if good generalization is to be guaranteed. In some imaging domains, however, labeled data with pixel- or voxel-level label accuracy are scarce due to the cost of acquiring them. This problem is exacerbated further in domains like medical imaging, where there is no single ground truth label, resulting in large amounts of repeat variability in the labels. Therefore, training reconstruction networks to generalize better by learning from both labeled and unlabeled examples (called semi-supervised learning) is problem of practical and theoretical interest. However, traditional semi-supervised learning methods for image reconstruction often necessitate handcrafting a differentiable regularizer specific to some given imaging problem, which can be extremely time-consuming. In this work, we propose "supervision by denoising" (SUD), a framework that enables us to supervise reconstruction models using their own denoised output as soft labels. SUD unifies stochastic averaging and spatial denoising techniques under a spatio-temporal denoising framework and alternates denoising and model weight update steps in an optimization framework for semi-supervision. As example applications, we apply SUD to two problems arising from biomedical imaging -- anatomical brain reconstruction (3D) and cortical parcellation (2D) -- to demonstrate a significant improvement in the image reconstructions over supervised-only and stochastic averaging baselines.

Ruangrawee Kitichotkul, Christopher A. Metzler, Frank Ong et al.

Convolutional neural networks (CNN) have emerged as a powerful tool for solving computational imaging reconstruction problems. However, CNNs are generally difficult-to-understand black-boxes. Accordingly, it is challenging to know when they will work and, more importantly, when they will fail. This limitation is a major barrier to their use in safety-critical applications like medical imaging: Is that blob in the reconstruction an artifact or a tumor? In this work we use Stein's unbiased risk estimate (SURE) to develop per-pixel confidence intervals, in the form of heatmaps, for compressive sensing reconstruction using the approximate message passing (AMP) framework with CNN-based denoisers. These heatmaps tell end-users how much to trust an image formed by a CNN, which could greatly improve the utility of CNNs in various computational imaging applications.

Gregory Ongie, Ajil Jalal, Christopher A. Metzler et al.

Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy that can be used to categorize different problems and reconstruction methods. Our taxonomy is organized along two central axes: (1) whether or not a forward model is known and to what extent it is used in training and testing, and (2) whether or not the learning is supervised or unsupervised, i.e., whether or not the training relies on access to matched ground truth image and measurement pairs. We also discuss the trade-offs associated with these different reconstruction approaches, caveats and common failure modes, plus open problems and avenues for future work.

Christopher A. Metzler, Gordon Wetzstein

This paper introduces and solves the simultaneous source separation and phase retrieval (S$^3$PR) problem. S$^3$PR is an important but largely unsolved problem in a number application domains, including microscopy, wireless communication, and imaging through scattering media, where one has multiple independent coherent sources whose phase is difficult to measure. In general, S$^3$PR is highly under-determined, non-convex, and difficult to solve. In this work, we demonstrate that by restricting the solutions to lie in the range of a deep generative model, we can constrain the search space sufficiently to solve S$^3$PR.

Christopher A. Metzler, David B. Lindell, Gordon Wetzstein

Non-line-of-sight (NLOS) imaging and tracking is an emerging technology that allows the shape or position of objects around corners or behind diffusers to be recovered from transient, time-of-flight measurements. However, existing NLOS approaches require the imaging system to scan a large area on a visible surface, where the indirect light paths of hidden objects are sampled. In many applications, such as robotic vision or autonomous driving, optical access to a large scanning area may not be available, which severely limits the practicality of existing NLOS techniques. Here, we propose a new approach, dubbed keyhole imaging, that captures a sequence of transient measurements along a single optical path, for example, through a keyhole. Assuming that the hidden object of interest moves during the acquisition time, we effectively capture a series of time-resolved projections of the object's shape from unknown viewpoints. We derive inverse methods based on expectation-maximization to recover the object's shape and location using these measurements. Then, with the help of long exposure times and retroreflective tape, we demonstrate successful experimental results with a prototype keyhole imaging system.

Christopher A. Metzler, Hayato Ikoma, Yifan Peng et al.

High-dynamic-range (HDR) imaging is crucial for many computer graphics and vision applications. Yet, acquiring HDR images with a single shot remains a challenging problem. Whereas modern deep learning approaches are successful at hallucinating plausible HDR content from a single low-dynamic-range (LDR) image, saturated scene details often cannot be faithfully recovered. Inspired by recent deep optical imaging approaches, we interpret this problem as jointly training an optical encoder and electronic decoder where the encoder is parameterized by the point spread function (PSF) of the lens, the bottleneck is the sensor with a limited dynamic range, and the decoder is a convolutional neural network (CNN). The lens surface is then jointly optimized with the CNN in a training phase; we fabricate this optimized optical element and attach it as a hardware add-on to a conventional camera during inference. In extensive simulations and with a physical prototype, we demonstrate that this end-to-end deep optical imaging approach to single-shot HDR imaging outperforms both purely CNN-based approaches and other PSF engineering approaches.

Christopher A. Metzler, Ali Mousavi, Richard G. Baraniuk

Compressive image recovery is a challenging problem that requires fast and accurate algorithms. Recently, neural networks have been applied to this problem with promising results. By exploiting massively parallel GPU processing architectures and oodles of training data, they can run orders of magnitude faster than existing techniques. However, these methods are largely unprincipled black boxes that are difficult to train and often-times specific to a single measurement matrix. It was recently demonstrated that iterative sparse-signal-recovery algorithms can be "unrolled" to form interpretable deep networks. Taking inspiration from this work, we develop a novel neural network architecture that mimics the behavior of the denoising-based approximate message passing (D-AMP) algorithm. We call this new network Learned D-AMP (LDAMP). The LDAMP network is easy to train, can be applied to a variety of different measurement matrices, and comes with a state-evolution heuristic that accurately predicts its performance. Most importantly, it outperforms the state-of-the-art BM3D-AMP and NLR-CS algorithms in terms of both accuracy and run time. At high resolutions, and when used with sensing matrices that have fast implementations, LDAMP runs over $50\times$ faster than BM3D-AMP and hundreds of times faster than NLR-CS.

Christopher A. Metzler, Arian Maleki, Richard G. Baraniuk

A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several decades, and as a result, today's denoisers can effectively remove large amounts of additive white Gaussian noise. A compressed sensing (CS) reconstruction algorithm seeks to recover a structured signal acquired using a small number of randomized measurements. Typical CS reconstruction algorithms can be cast as iteratively estimating a signal from a perturbed observation. This paper answers a natural question: How can one effectively employ a generic denoiser in a CS reconstruction algorithm? In response, we develop an extension of the approximate message passing (AMP) framework, called Denoising-based AMP (D-AMP), that can integrate a wide class of denoisers within its iterations. We demonstrate that, when used with a high performance denoiser for natural images, D-AMP offers state-of-the-art CS recovery performance while operating tens of times faster than competing methods. We explain the exceptional performance of D-AMP by analyzing some of its theoretical features. A key element in D-AMP is the use of an appropriate Onsager correction term in its iterations, which coerces the signal perturbation at each iteration to be very close to the white Gaussian noise that denoisers are typically designed to remove.