We introduce Gaussian representations for videos (GaRV), a novel video encoding and decoding scheme based upon 3D Gaussians. Unlike traditional representations, which encode videos as sequences of frames, or neural representations, which encode videos within the weights of a neural network, we encode videos as a collection of 3D Gaussians within a space-time volume. The key advantage of our approach is that it enables efficient and flexible rasterization-based video decoding. With a slight drop in overall compression rate, GaRV offers an 8-50× improvement in decoding time and 2.5-15× reduction in GPU memory compared with neural counterparts. Existing Gaussian video techniques require 2-30× more disk space, while also using more GPU resources than GaRV. Moreover, GaRV offers unique flexibility in how and when pixels are decoded: One can non-sequentially decode frames/regions without penalty and can selectively decode regions at high-resolution to enable low-cost foveated video decoding.

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 flash-informed reflection separation iteratively in a low-dimensional latent space. Specifically, Flash-Split consists of two stages. Stage 1 separates the reflection latent and transmission latent via a dual-branch diffusion model that is conditioned on an encoded flash/no-flash latent pair. This stage effectively mitigates the flash/no-flash misalignment issue. Stage 2 restores high-resolution, faithful details to the separated latents via a cross-latent decoding process that is conditioned on the original images before separation. We validate Flash-Split on challenging real-world scenes and demonstrate it significantly outperforms existing methods. Our project webpage is at https://flash-split.github.io/.

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.

Text-to-image diffusion models excel at generating diverse portraits, but lack intuitive shadow control. Existing editing approaches, as post-processing, struggle to offer effective manipulation across diverse styles. Additionally, these methods either rely on expensive real-world light-stage data collection or require extensive computational resources for training. To address these limitations, we introduce Shadow Director, a method that extracts and manipulates hidden shadow attributes within well-trained diffusion models. Our approach uses a small estimation network that requires only a few thousand synthetic images and hours of training-no costly real-world light-stage data needed. Shadow Director enables parametric and intuitive control over shadow shape, placement, and intensity during portrait generation while preserving artistic integrity and identity across diverse styles. Despite training only on synthetic data built on real-world identities, it generalizes effectively to generated portraits with diverse styles, making it a more accessible and resource-friendly solution.

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.

Differentiable 3D-Gaussian splatting (GS) is emerging as a prominent technique in computer vision and graphics for reconstructing 3D scenes. GS represents a scene as a set of 3D Gaussians with varying opacities and employs a computationally efficient splatting operation along with analytical derivatives to compute the 3D Gaussian parameters given scene images captured from various viewpoints. Unfortunately, capturing surround view ($\text{360}^{\circ }$360∘ viewpoint) images is impossible or impractical in many real-world imaging scenarios, including underwater imaging, rooms inside a building, and autonomous navigation. In these restricted baseline imaging scenarios, the GS algorithm suffers from a well-known 'missing cone' problem, which results in poor reconstruction along the depth axis. In this paper, we demonstrate that using transient data (from sonars) allows us to address the missing cone problem by sampling high-frequency data along the depth axis. We extend the Gaussian splatting algorithms for two commonly used sonars and propose fusion algorithms that simultaneously utilize RGB camera data and sonar data. Through simulations, emulations, and hardware experiments across various imaging scenarios, we show that the proposed fusion algorithms lead to significantly better novel view synthesis (5 dB improvement in PSNR) and 3D geometry reconstruction (60% lower Chamfer distance).

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 to supervise reconstruction models using their own denoised output as 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 from biomedical imaging-anatomical brain reconstruction (3D) and cortical parcellation (2D)-to demonstrate a significant improvement in reconstruction over supervised-only and ensembling baselines.

The reflective nature of the human eye is an under-appreciated source of information about what the world around us looks like. By imaging the eyes of a moving person, we capture multiple views of a scene outside the camera's direct line of sight through the reflections in the eyes. In this paper, we reconstruct a radiance field beyond the camera's line of sight using portrait images containing eye reflections. This task is challenging due to 1) the difficulty of accurately estimating eye poses and 2) the entangled appearance of the iris textures and the scene reflections. To address these, our method jointly optimizes the cornea poses, the radiance field depicting the scene, and the observer's eye iris texture. We further present a regularization prior on the iris texture to improve scene reconstruction quality. Through various experiments on synthetic and real-world captures featuring people with varied eye colors, and lighting conditions, we demonstrate the feasibility of our approach to recover the radiance field using cornea reflections.

Point-spread-function (PSF) engineering is a well-established computational imaging technique that uses phase masks and other optical elements to embed extra information (e.g., depth) into the images captured by conventional CMOS image sensors. To date, however, PSF-engineering has not been applied to neuromorphic event cameras; a powerful new image sensing technology that responds to changes in the log-intensity of light. This paper establishes theoretical limits (Cramér Rao bounds) on 3D point localization and tracking with PSF-engineered event cameras. Using these bounds, we first demonstrate that existing Fisher phase masks are already near-optimal for localizing static flashing point sources (e.g., blinking fluorescent molecules). We then demonstrate that existing designs are sub-optimal for tracking moving point sources and proceed to use our theory to design optimal phase masks and binary amplitude masks for this task. To overcome the non-convexity of the design problem, we leverage novel implicit neural representation based parameterizations of the phase and amplitude masks. We demonstrate the efficacy of our designs through extensive simulations. We also validate our method with a simple prototype.

Imaging through scattering media is a fundamental and pervasive challenge infields ranging from medical diagnos-tics to astronomy. A promising strategy to overcome this challenge is wavefront modulation, which induces measure-ment diversity during image acquisition. Despite its importance, designing optimal wavefront modulations to image through scattering remains under-explored. This paper in-troduces a novel learning-based framework to address the gap. Our approach jointly optimizes wavefront modulations and a computationally lightweight feedforward “proxy” re-construction 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 un-seen scattering scenarios and exhibit remarkable versatility. During deployment, the learned modulations can be decou-pled from the proxy network to augment other more computationally expensive restoration algorithms. Through ex-tensive experiments, we demonstrate our approach signifi-cantly advances the state of the art in imaging through scat-tering media. Our project webpage is at https://wavemo-2024.github.io/.

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.

Atmospheric turbulence, caused by random fluctuations in the atmosphere's refractive index, introduces complex spatio-temporal distortions in imagery captured at long range. Video Atmospheric Turbulence Mitigation (ATM) aims to restore videos affected by these distortions. However, existing video ATM methods, both supervised and self-supervised, struggle to maintain temporally consistent mitigation across frames, leading to visually incoherent results. This limitation arises from the stochastic nature of atmospheric turbulence, which varies across space and time. Inspired by the observation that atmospheric turbulence induces high-frequency temporal variations, we propose ConVRT, a novel framework for consistent video restoration through turbulence. ConVRT introduces a neural video representation that explicitly decouples spatial and temporal information into a spatial content field and a temporal deformation field, enabling targeted regularization of the network's temporal representation capability. By leveraging the low-pass filtering properties of the regularized temporal representations, ConVRT effectively mitigates turbulence-induced temporal frequency variations and promotes temporal consistency. Furthermore, our training framework seamlessly integrates supervised pre-training on synthetic turbulence data with self-supervised learning on real-world videos, significantly improving the temporally consistent mitigation of ATM methods on diverse real-world data. More information can be found on our project page: https://convrt-2024.github.io/

Despite recent advances, developing general-purpose universal denoising and artifact-removal networks remains largely an open problem: Given fixed network weights, one inherently trades-off specialization at one task (e.g., removing Poisson noise) for performance at another (e.g., removing speckle noise). In addition, training such a network is challenging due to the curse of dimensionality: As one increases the dimensions of the specification-space (i.e., the number of parameters needed to describe the noise distribution) the number of unique specifications one needs to train for grows exponentially. Uniformly sampling this space will result in a network that does well at very challenging problem specifications but poorly at easy problem specifications, where even large errors will have a small effect on the overall mean squared error. In this work we propose training denoising networks using an adaptive-sampling/active-learning strategy. Our work improves upon a recently proposed universal denoiser training strategy by extending these results to higher dimensions and by incorporating a polynomial approximation of the true specification-loss landscape. This approximation allows us to reduce training times by almost two orders of magnitude. We test our method on simulated joint Poisson-Gaussian-Speckle noise and demonstrate that with our proposed training strategy, a single blind, generalist denoiser network can achieve peak signal-to-noise ratios within a uniform bound of specialized denoiser networks across a large range of operating conditions. We also capture a small dataset of images with varying amounts of joint Poisson-Gaussian-Speckle noise and demonstrate that a universal denoiser trained using our adaptive-sampling strategy outperforms uniformly trained baselines.

Point-spread-function (PSF) engineering is a powerful computational imaging technique 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 leverage this increased expressiveness to offer substantially improved monocular depth estimation and extended depth-of-field imaging performance.

For image recovery problems, plug-and-play (PnP) methods have been developed that replace the proximal step in an optimization algorithm with a call to an application-specific denoiser, often implemented using a deep neural network. Although such methods have been successful, they can be improved. For example, the denoiser is often trained using white Gaussian noise, while PnP's denoiser input error is often far from white and Gaussian, with statistics that are difficult to predict from iteration to iteration. PnP methods based on approximate message passing (AMP) are an exception, but only when the forward operator behaves like a large random matrix. In this work, we design a PnP method using the expectation consistent (EC) approximation algorithm, a generalization of AMP, that offers predictable error statistics at each iteration, from which a deep-net denoiser can be effectively trained.

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.

This paper introduces and solves the simultaneous source separation and phase retrieval (S3PR) problem. S3PR 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, S3PR 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 S3PR.Code associated with this work is available at https://github.com/computational-imaging/DeepS3PR. An extended version of this work is available at https://arxiv.org/abs/2002.05856.

Plug and play (P&P) algorithms iteratively apply highly optimized image denoisers to impose priors and solve computational image reconstruction problems, to great effect. However, in general the "effective noise", that is the difference between the true signal and the intermediate solution, within the iterations of P&P algorithms is neither Gaussian nor white. This fact makes existing denoising algorithms suboptimal.In this work, we propose a CNN architecture for removing colored Gaussian noise and combine it with the recently proposed VDAMP algorithm, whose effective noise follows a predictable colored Gaussian distribution. We apply the resulting denoising-based VDAMP (D-VDAMP) algorithm to variable density sampled compressive MRI where it substantially outperforms existing techniques.

Monocular depth estimation remains a challenging problem, despite significant advances in neural network architectures that leverage pictorial depth cues alone. Inspired by depth from defocus and emerging point spread function engineering approaches that optimize programmable optics end-to-end with depth estimation networks, we propose a new and improved framework for depth estimation from a single RGB image using a learned phase-coded aperture. Our optimized aperture design uses rotational symmetry constraints for computational efficiency, and we jointly train the optics and the network using an occlusion-aware image formation model that provides more accurate defocus blur at depth discontinuities than previous techniques do. Using this framework and a custom prototype camera, we demonstrate state-of-the art image and depth estimation quality among end-to-end optimized computational cameras in simulation and experiment.

High-dynamic-range (HDR) imaging is crucial for many 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.

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 developing 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 transmission matrix describes the input-output relationship of a complex wavefront as it passes through/reflects off a multiple-scattering medium, such as frosted glass or a painted wall. Knowing a medium's transmission matrix enables one to image through the medium, send signals through the medium, or even use the medium as a lens. The double phase retrieval method is a recently proposed technique to learn a medium's transmission matrix that avoids difficult-to-capture interferometric measurements. Unfortunately, to perform high resolution imaging, existing double phase retrieval methods require (1) a large number of measurements and (2) an unreasonable amount of computation. In this work we focus on the latter of these two problems and reduce computation times with two distinct methods: First, we develop a new phase retrieval algorithm that is significantly faster than existing methods, especially when used with an amplitude-only spatial light modulator (SLM). Second, we calibrate the system using a phase-only SLM, rather than an amplitude-only SLM which was used in previous double phase retrieval experiments. This seemingly trivial change enables us to use a far faster class of phase retrieval algorithms. As a result of these advances, we achieve a 100x reduction in computation times, thereby allowing us to image through scattering media at state-of-the-art resolutions. In addition to these advances, we also release the first publicly available transmission matrix dataset. This contribution will enable phase retrieval researchers to apply their algorithms to real data. Of particular interest to this community, our measurement vectors are naturally i.i.d. subgaussian, i.e., no coded diffraction pattern is required.

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 {\em 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.

The explosion of computational imaging has seen the frontier of image processing move past linear problems, like denoising and deblurring, and towards non-linear problems such as phase retrieval. There has a been a corresponding research thrust into non-linear image recovery algorithms, but in many ways this research is stuck where linear problem research was twenty years ago: Models, if used at all, are simple designs like sparsity or smoothness. In this paper we use denoisers to impose elaborate and accurate models in order to perform inference on generalized linear systems. More specifically, we use the state-of-the-art BM3D denoiser within the Generalized Approximate Message Passing (GAMP) framework to solve compressive phase retrieval in a variety of different contexts. Our method demonstrates recovery performance equivalent to existing techniques using fewer than half as many measurements. This dramatic improvement in compressive phase retrieval performance opens the door for a whole new class of imaging systems.

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, todays 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 the 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.

A denoising algorithm seeks to remove perturbations or errors from a signal. The last three decades have seen extensive research devoted to this arena, and as a result, today's denoisers are highly optimized algorithms that effectively remove large amounts of additive white Gaussian noise. A compressive sensing (CS) reconstruction algorithm seeks to recover a structured signal acquired from 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 a denoising-based approximate message passing (D-AMP) algorithm that is capable of high-performance reconstruction. We demonstrate using the high performance BM3D denoiser that D-AMP offers state-of-the-art CS recovery performance for natural images (on average 9dB better than sparsity-based algorithms), while operating tens of times faster than the only competitive method. A critical insight in our approach is the use of an appropriate Onsager correction term in the D-AMP 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. On the analytical side, we develop a new state evolution framework for deterministic signals that accurately predicts the performance of D-AMP and enables us to derive several useful theoretical features.