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The proliferation of single-photon image sensors has opened the door to a plethora of high-speed and low-light imaging applications. However, data collected by these sensors are often 1-bit or few-bit, and corrupted by noise and strong motion. Conventional video restoration methods are not designed to handle this situation, while specialized quanta burst algorithms have limited performance when the number of input frames is low. In this paper, we introduce Quanta Video Restoration (QUIVER), an end-to-end trainable network built on the core ideas of classical quanta restoration methods, i.e., pre-filtering, flow estimation, fusion, and refinement. We also collect and publish I2-2000FPS, a high-speed video dataset with the highest temporal resolution of 2000 frames-per-second, for training and testing. On simulated and real data, QUIVER outperforms existing quanta restoration methods by a significant margin. Code and dataset available at https://github.com/chennuriprateek/Quanta_Video_Restoration-QUIVER-

Depth estimation using a single-photon LiDAR is often solved by a matched filter. It is, however, error-prone in the presence of background noise. A commonly used technique to reject background noise is the rank-ordered mean (ROM) filter previously reported by Shin \textit{et al.} (2015). ROM rejects noisy photon arrival timestamps by selecting only a small range of them around the median statistics within its local neighborhood. Despite the promising performance of ROM, its theoretical performance limit is unknown. In this paper, we theoretically characterize the ROM performance by showing that ROM fails when the reflectivity drops below a threshold predetermined by the depth and signal-to-background ratio, and its accuracy undergoes a phase transition at the cutoff. Based on our theory, we propose an improved signal extraction technique by selecting tight timestamp clusters. Experimental results show that the proposed algorithm improves depth estimation performance over ROM by 3 orders of magnitude at the same signal intensities, and achieves high image fidelity at noise levels as high as 17 times that of signal., Comment: 6 pages, 7 figures, submitted to the IEEE 26th International Workshop on Multimedia Signal Processing (MMSP)

In single-photon light detection and ranging (SP-LiDAR) systems, the histogram distortion due to hardware dead time fundamentally limits the precision of depth estimation. To compensate for the dead time effects, the photon registration distribution is typically modeled based on the Markov chain self-excitation process. However, this is a discrete process and it is computationally expensive, thus hindering potential neural network applications and fast simulations. In this paper, we overcome the modeling challenge by proposing a continuous parametric model. We introduce a Gaussian-uniform mixture model (GUMM) and periodic padding to address high noise floors and noise slopes respectively. By deriving and implementing a customized expectation maximization (EM) algorithm, we achieve accurate histogram matching in scenarios that were deemed difficult in the literature.

The astonishing development of single-photon cameras has created an unprecedented opportunity for scientific and industrial imaging. However, the high data throughput generated by these 1-bit sensors creates a significant bottleneck for low-power applications. In this paper, we explore the possibility of generating a color image from a single binary frame of a single-photon camera. We evidently find this problem being particularly difficult to standard colorization approaches due to the substantial degree of exposure variation. The core innovation of our paper is an exposure synthesis model framed under a neural ordinary differential equation (Neural ODE) that allows us to generate a continuum of exposures from a single observation. This innovation ensures consistent exposure in binary images that colorizers take on, resulting in notably enhanced colorization. We demonstrate applications of the method in single-image and burst colorization and show superior generative performance over baselines. Project website can be found at https://vishal-s-p.github.io/projects/2023/generative_quanta_color.html., Comment: Accepted at IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2024

The astonishing growth of generative tools in recent years has empowered many exciting applications in text-to-image generation and text-to-video generation. The underlying principle behind these generative tools is the concept of diffusion, a particular sampling mechanism that has overcome some shortcomings that were deemed difficult in the previous approaches. The goal of this tutorial is to discuss the essential ideas underlying the diffusion models. The target audience of this tutorial includes undergraduate and graduate students who are interested in doing research on diffusion models or applying these models to solve other problems.

Single-photon Light Detection and Ranging (LiDAR) systems are often equipped with an array of detectors for improved spatial resolution and sensing speed. However, given a fixed amount of flux produced by the laser transmitter across the scene, the per-pixel Signal-to-Noise Ratio (SNR) will decrease when more pixels are packed in a unit space. This presents a fundamental trade-off between the spatial resolution of the sensor array and the SNR received at each pixel. Theoretical characterization of this fundamental limit is explored. By deriving the photon arrival statistics and introducing a series of new approximation techniques, the Mean Squared Error (MSE) of the maximum-likelihood estimator of the time delay is derived. The theoretical predictions align well with simulations and real data.

Working from a Poisson-Gaussian noise model, a multi-sample extension of the Photon Counting Histogram Expectation Maximization (PCH-EM) algorithm is derived as a general-purpose alternative to the Photon Transfer (PT) method. This algorithm is derived from the same model, requires the same experimental data, and estimates the same sensor performance parameters as the time-tested PT method, all while obtaining lower uncertainty estimates. It is shown that as read noise becomes large, multiple data samples are necessary to capture enough information about the parameters of a device under test, justifying the need for a multi-sample extension. An estimation procedure is devised consisting of initial PT characterization followed by repeated iteration of PCH-EM to demonstrate the improvement in estimate uncertainty achievable with PCH-EM; particularly in the regime of Deep Sub-Electron Read Noise (DSERN). A statistical argument based on the information theoretic concept of sufficiency is formulated to explain how PT data reduction procedures discard information contained in raw sensor data, thus explaining why the proposed algorithm is able to obtain lower uncertainty estimates of key sensor performance parameters such as read noise and conversion gain. Experimental data captured from a CMOS quanta image sensor with DSERN is then used to demonstrate the algorithm's usage and validate the underlying theory and statistical model. In support of the reproducible research effort, the code associated with this work can be obtained on the MathWorks File Exchange (Hendrickson et al., 2024)., Comment: 14 pages, 8 figures

Recovering images distorted by atmospheric turbulence is a challenging inverse problem due to the stochastic nature of turbulence. Although numerous turbulence mitigation (TM) algorithms have been proposed, their efficiency and generalization to real-world dynamic scenarios remain severely limited. Building upon the intuitions of classical TM algorithms, we present the Deep Atmospheric TUrbulence Mitigation network (DATUM). DATUM aims to overcome major challenges when transitioning from classical to deep learning approaches. By carefully integrating the merits of classical multi-frame TM methods into a deep network structure, we demonstrate that DATUM can efficiently perform long-range temporal aggregation using a recurrent fashion, while deformable attention and temporal-channel attention seamlessly facilitate pixel registration and lucky imaging. With additional supervision, tilt and blur degradation can be jointly mitigated. These inductive biases empower DATUM to significantly outperform existing methods while delivering a tenfold increase in processing speed. A large-scale training dataset, ATSyn, is presented as a co-invention to enable generalization in real turbulence. Our code and datasets are available at https://xg416.github.io/DATUM., Comment: Accepted by CVPR 2024, project page https://xg416.github.io/DATUM/

Blind deconvolution problems are severely ill-posed because neither the underlying signal nor the forward operator are not known exactly. Conventionally, these problems are solved by alternating between estimation of the image and kernel while keeping the other fixed. In this paper, we show that this framework is flawed because of its tendency to get trapped in local minima and, instead, suggest the use of a kernel estimation strategy with a non-blind solver. This framework is employed by a diffusion method which is trained to sample the blur kernel from the conditional distribution with guidance from a pre-trained non-blind solver. The proposed diffusion method leads to state-of-the-art results on both synthetic and real blur datasets.

Non-blind image deconvolution has been studied for several decades but most of the existing work focuses on blur instead of noise. In photon-limited conditions, however, the excessive amount of shot noise makes traditional deconvolution algorithms fail. In searching for reasons why these methods fail, we present a systematic analysis of the Poisson non-blind deconvolution algorithms reported in the literature, covering both classical and deep learning methods. We compile a list of five "secrets" highlighting the do's and don'ts when designing algorithms. Based on this analysis, we build a proof-of-concept method by combining the five secrets. We find that the new method performs on par with some of the latest methods while outperforming some older ones., Comment: Under submission at Transactions on Computational Imaging

At the pinnacle of computational imaging is the co-optimization of camera and algorithm. This, however, is not the only form of computational imaging. In problems such as imaging through adverse weather, the bigger challenge is how to accurately simulate the forward degradation process so that we can synthesize data to train reconstruction models and/or integrating the forward model as part of the reconstruction algorithm. This article introduces the concept of computational image formation (CIF). Compared to the standard inverse problems where the goal is to recover the latent image $x$ from the observation $y = G(x)$, CIF shifts the focus to designing an approximate mapping $H$ such that $H \approx G$ while giving a good image reconstruction result. The word "computational" highlights the fact that the image formation is now replaced by a numerical simulator. While matching the mother nature remains an important goal, CIF pays even greater attention on strategically choosing an $H$ so that the reconstruction performance is maximized. The goal of this article is to conceptualize the idea of CIF by elaborating on its meaning and implications. The first part of the article is a discussion on the four attributes of a CIF simulator: accurate enough to mimic $G$, fast enough to be integrated as part of the reconstruction, provides a well-posed inverse problem when plugged into the reconstruction, and differentiable to allow backpropagation. The second part of the article is a detailed case study based on imaging through atmospheric turbulence. A plethora of simulators, old and new ones, are discussed. The third part of the article is a collection of other examples that fall into the category of CIF, including imaging through bad weather, dynamic vision sensors, and differentiable optics. Finally, thoughts about the future direction and recommendations to the community are shared.

Image distortion by atmospheric turbulence is a stochastic degradation, which is a critical problem in long-range optical imaging systems. A number of research has been conducted during the past decades, including model-based and emerging deep-learning solutions with the help of synthetic data. Although fast and physics-grounded simulation tools have been introduced to help the deep-learning models adapt to real-world turbulence conditions recently, the training of such models only relies on the synthetic data and ground truth pairs. This paper proposes the Physics-integrated Restoration Network (PiRN) to bring the physics-based simulator directly into the training process to help the network to disentangle the stochasticity from the degradation and the underlying image. Furthermore, to overcome the ``average effect" introduced by deterministic models and the domain gap between the synthetic and real-world degradation, we further introduce PiRN with Stochastic Refinement (PiRN-SR) to boost its perceptual quality. Overall, our PiRN and PiRN-SR improve the generalization to real-world unknown turbulence conditions and provide a state-of-the-art restoration in both pixel-wise accuracy and perceptual quality. Our codes are available at \url{https://github.com/VITA-Group/PiRN}., Comment: Accepted by ICCV 2023

The advancement of new digital image sensors has enabled the design of exposure multiplexing schemes where a single image capture can have multiple exposures and conversion gains in an interlaced format, similar to that of a Bayer color filter array. In this paper, we ask the question of how to design such multiplexing schemes for adaptive high-dynamic range (HDR) imaging where the multiplexing scheme can be updated according to the scenes. We present two new findings. (i) We address the problem of design optimality. We show that given a multiplex pattern, the conventional optimality criteria based on the input/output-referred signal-to-noise ratio (SNR) of the independently measured pixels can lead to flawed decisions because it cannot encapsulate the location of the saturated pixels. We overcome the issue by proposing a new concept known as the spatially varying exposure risk (SVE-Risk) which is a pseudo-idealistic quantification of the amount of recoverable pixels. We present an efficient enumeration algorithm to select the optimal multiplex patterns. (ii) We report a design universality observation that the design of the multiplex pattern can be decoupled from the image reconstruction algorithm. This is a significant departure from the recent literature that the multiplex pattern should be jointly optimized with the reconstruction algorithm. Our finding suggests that in the context of exposure multiplexing, an end-to-end training may not be necessary.

For the simulation of anisoplanatic optical turbulence, split-step propagation is the gold standard. Within the context of the degradations being limited to phase distortions, one instead may focus on generating the phase realizations directly, a method which has been utilized in previous so-called multi-aperture simulations. Presently, this modality assumes a constant $C_n^2$ profile. This work presents an alternative derivation for Zernike correlations under anisoplanatic conditions. Multi-aperture simulation may easily incorporate these correlations into its framework and achieve a significantly higher degree of accuracy with a minimal increase in time. We additionally use our developed methodology to explain previously reported discrepancies in an empirical implementation of split-step with the analytic tilt correlation. Finally, we outline a major limitation for Zernike-based simulation which still remains.

While today's high dynamic range (HDR) image fusion algorithms are capable of blending multiple exposures, the acquisition is often controlled so that the dynamic range within one exposure is narrow. For HDR imaging in photon-limited situations, the dynamic range can be enormous and the noise within one exposure is spatially varying. Existing image denoising algorithms and HDR fusion algorithms both fail to handle this situation, leading to severe limitations in low-light HDR imaging. This paper presents two contributions. Firstly, we identify the source of the problem. We find that the issue is associated with the co-existence of (1) spatially varying signal-to-noise ratio, especially the excessive noise due to very dark regions, and (2) a wide luminance range within each exposure. We show that while the issue can be handled by a bank of denoisers, the complexity is high. Secondly, we propose a new method called the spatially varying high dynamic range (SV-HDR) fusion network to simultaneously denoise and fuse images. We introduce a new exposure-shared block within our custom-designed multi-scale transformer framework. In a variety of testing conditions, the performance of the proposed SV-HDR is better than the existing methods.

In this paper, we study how the granularity of pretraining labels affects the generalization of deep neural networks in image classification tasks. We focus on the "fine-to-coarse" transfer learning setting, where the pretraining label space is more fine-grained than that of the target problem. Empirically, we show that pretraining on the leaf labels of ImageNet21k produces better transfer results on ImageNet1k than pretraining on other coarser granularity levels, which supports the common practice used in the community. Theoretically, we explain the benefit of fine-grained pretraining by proving that, for a data distribution satisfying certain hierarchy conditions, 1) coarse-grained pretraining only allows a neural network to learn the "common" or "easy-to-learn" features well, while 2) fine-grained pretraining helps the network learn the "rarer" or "fine-grained" features in addition to the common ones, thus improving its accuracy on hard downstream test samples in which common features are missing or weak in strength. Furthermore, we perform comprehensive experiments using the label hierarchies of iNaturalist 2021 and observe that the following conditions, in addition to proper choice of label granularity, enable the transfer to work well in practice: 1) the pretraining dataset needs to have a meaningful label hierarchy, and 2) the pretraining and target label functions need to align well.

A spatially varying blur kernel $h(\mathbf{x},\mathbf{u})$ is specified by an input coordinate $\mathbf{u} \in \mathbb{R}^2$ and an output coordinate $\mathbf{x} \in \mathbb{R}^2$. For computational efficiency, we sometimes write $h(\mathbf{x},\mathbf{u})$ as a linear combination of spatially invariant basis functions. The associated pixelwise coefficients, however, can be indexed by either the input coordinate or the output coordinate. While appearing subtle, the two indexing schemes will lead to two different forms of convolutions known as scattering and gathering, respectively. We discuss the origin of the operations. We discuss conditions under which the two operations are identical. We show that scattering is more suitable for simulating how light propagates and gathering is more suitable for image filtering such as denoising.

Images taken in a low light condition with the presence of camera shake suffer from motion blur and photon shot noise. While state-of-the-art image restoration networks show promising results, they are largely limited to well-illuminated scenes and their performance drops significantly when photon shot noise is strong. In this paper, we propose a new blur estimation technique customized for photon-limited conditions. The proposed method employs a gradient-based backpropagation method to estimate the blur kernel. By modeling the blur kernel using a low-dimensional representation with the key points on the motion trajectory, we significantly reduce the search space and improve the regularity of the kernel estimation problem. When plugged into an iterative framework, our novel low-dimensional representation provides improved kernel estimates and hence significantly better deconvolution performance when compared to end-to-end trained neural networks. The source code and pretrained models are available at \url{https://github.com/sanghviyashiitb/structured-kernel-cvpr23}, Comment: main document and supplementary; accepted at CVPR2023

Numerical simulation of atmospheric turbulence is one of the biggest bottlenecks in developing computational techniques for solving the inverse problem in long-range imaging. The classical split-step method is based upon numerical wave propagation which splits the propagation path into many segments and propagates every pixel in each segment individually via the Fresnel integral. This repeated evaluation becomes increasingly time-consuming for larger images. As a result, the split-step simulation is often done only on a sparse grid of points followed by an interpolation to the other pixels. Even so, the computation is expensive for real-time applications. In this paper, we present a new simulation method that enables \emph{real-time} processing over a \emph{dense} grid of points. Building upon the recently developed multi-aperture model and the phase-to-space transform, we overcome the memory bottleneck in drawing random samples from the Zernike correlation tensor. We show that the cross-correlation of the Zernike modes has an insignificant contribution to the statistics of the random samples. By approximating these cross-correlation blocks in the Zernike tensor, we restore the homogeneity of the tensor which then enables Fourier-based random sampling. On a $512\times512$ image, the new simulator achieves 0.025 seconds per frame over a dense field. On a $3840 \times 2160$ image which would have taken 13 hours to simulate using the split-step method, the new simulator can run at approximately 60 seconds per frame.

The one-bit quanta image sensor (QIS) is a photon-counting device that captures image intensities using binary bits. Assuming that the analog voltage generated at the floating diffusion of the photodiode follows a Poisson-Gaussian distribution, the sensor produces either a ``1'' if the voltage is above a certain threshold or ``0'' if it is below the threshold. The concept of this binary sensor has been proposed for more than a decade, and physical devices have been built to realize the concept. However, what benefits does a one-bit QIS offer compared to a conventional multi-bit CMOS image sensor? Besides the known empirical results, are there theoretical proofs to support these findings? The goal of this paper is to provide new theoretical support from a signal processing perspective. In particular, it is theoretically found that the sensor can offer three benefits: (1) Low-light: One-bit QIS performs better at low-light because it has a low read noise, and its one-bit quantization can produce an error-free measurement. However, this requires the exposure time to be appropriately configured. (2) Frame rate: One-bit sensors can operate at a much higher speed because a response is generated as soon as a photon is detected. However, in the presence of read noise, there exists an optimal frame rate beyond which the performance will degrade. A Closed-form expression of the optimal frame rate is derived. (3) Dynamic range: One-bit QIS offers a higher dynamic range. The benefit is brought by two complementary characteristics of the sensor: nonlinearity and exposure bracketing. The decoupling of the two factors is theoretically proved, and closed-form expressions are derived.

Blind deconvolution is a challenging problem, but in low-light it is even more difficult. Existing algorithms, both classical and deep-learning based, are not designed for this condition. When the photon shot noise is strong, conventional deconvolution methods fail because (1) the image does not have enough signal-to-noise ratio to perform the blur estimation; (2) While deep neural networks are powerful, many of them do not consider the forward process. When the noise is strong, these networks fail to simultaneously deblur and denoise; (3) While iterative schemes are known to be robust in the classical frameworks, they are seldom considered in deep neural networks because it requires a differentiable non-blind solver. This paper addresses the above challenges by presenting an \emph{unsupervised} blind deconvolution method. At the core of this method is a reformulation of the general blind deconvolution framework from the conventional image-kernel alternating minimization to a purely kernel-based minimization. This kernel-based minimization leads to a new iterative scheme that backpropagates an unsupervised loss through a pre-trained non-blind solver to update the blur kernel. Experimental results show that the proposed framework achieves superior results than state-of-the-art blind deconvolution algorithms in low-light conditions., Comment: accepted at Transactions on Computational Imaging

Image restoration algorithms for atmospheric turbulence are known to be much more challenging to design than traditional ones such as blur or noise because the distortion caused by the turbulence is an entanglement of spatially varying blur, geometric distortion, and sensor noise. Existing CNN-based restoration methods built upon convolutional kernels with static weights are insufficient to handle the spatially dynamical atmospheric turbulence effect. To address this problem, in this paper, we propose a physics-inspired transformer model for imaging through atmospheric turbulence. The proposed network utilizes the power of transformer blocks to jointly extract a dynamical turbulence distortion map and restore a turbulence-free image. In addition, recognizing the lack of a comprehensive dataset, we collect and present two new real-world turbulence datasets that allow for evaluation with both classical objective metrics (e.g., PSNR and SSIM) and a new task-driven metric using text recognition accuracy. Both real testing sets and all related code will be made publicly available., Comment: This paper is accepted as a poster at ECCV 2022

Restoring images distorted by atmospheric turbulence is a ubiquitous problem in long-range imaging applications. While existing deep-learning-based methods have demonstrated promising results in specific testing conditions, they suffer from three limitations: (1) lack of generalization capability from synthetic training data to real turbulence data; (2) failure to scale, hence causing memory and speed challenges when extending the idea to a large number of frames; (3) lack of a fast and accurate simulator to generate data for training neural networks. In this paper, we introduce the turbulence mitigation transformer (TMT) that explicitly addresses these issues. TMT brings three contributions: Firstly, TMT explicitly uses turbulence physics by decoupling the turbulence degradation and introducing a multi-scale loss for removing distortion, thus improving effectiveness. Secondly, TMT presents a new attention module along the temporal axis to extract extra features efficiently, thus improving memory and speed. Thirdly, TMT introduces a new simulator based on the Fourier sampler, temporal correlation, and flexible kernel size, thus improving our capability to synthesize better training data. TMT outperforms state-of-the-art video restoration models, especially in generalizing from synthetic to real turbulence data. Code, videos, and datasets are available at \href{https://xg416.github.io/TMT}{https://xg416.github.io/TMT}., Comment: Accepted by IEEE Transactions on Computational Imaging; project page: https://xg416.github.io/TMT/

Imaging at a long distance often requires advanced image restoration algorithms to compensate for the distortions caused by atmospheric turbulence. However, unlike many standard restoration problems such as deconvolution, the forward image formation model of the atmospheric turbulence does not have a simple expression. Thanks to the Zernike representation of the phase, one can show that the forward model is a combination of tilt (pixel shifting due to the linear phase terms) and blur (image smoothing due to the high order aberrations). Confusions then arise between the ordering of the two operators. Should the model be tilt-then-blur, or blur-then-tilt? Some papers in the literature say that the model is tilt-then-blur, whereas more papers say that it is blur-then-tilt. This paper clarifies the differences between the two and discusses why the tilt-then-blur is the correct model. Recommendations are given to the research community.

The one-bit quanta image sensor is a photon-counting device that produces binary measurements where each bit represents the presence or absence of a photon. In the presence of read noise, the sensor quantizes the analog voltage into the binary bits using a threshold value $q$. The average number of ones in the bitstream is known as the bit-density and is often the sufficient statistics for signal estimation. An intriguing phenomenon is observed when the quanta exposure is at the unity and the threshold is $q = 0.5$. The bit-density demonstrates a complete insensitivity as long as the read noise level does not exceeds a certain limit. In other words, the bit density stays at a constant independent of the amount of read noise. This paper provides a mathematical explanation of the phenomenon by deriving conditions under which the phenomenon happens. It was found that the insensitivity holds when some forms of the symmetry of the underlying Poisson-Gaussian distribution holds.

The signal-to-noise ratio (SNR) is a fundamental tool to measure the performance of an image sensor. However, confusions sometimes arise between the two types of SNRs. The first one is the output-referred SNR which measures the ratio between the signal and the noise seen at the sensor's output. This SNR is easy to compute, and it is linear in the log-log scale for most image sensors. The second SNR is the exposure-referred SNR, also known as the input-referred SNR. This SNR considers the noise at the input by including a derivative term to the output-referred SNR. The two SNRs have similar behaviors for sensors with a large full-well capacity. However, for sensors with a small full-well capacity, the exposure-referred SNR can capture some behaviors that the output-referred SNR cannot. While the exposure-referred SNR has been known and used by the industry for a long time, a theoretically rigorous derivation from a signal processing perspective is lacking. In particular, while various equations can be found in different sources of the literature, there is currently no paper that attempts to assemble, derive, and organize these equations in one place. This paper aims to fill the gap by answering four questions: (1) How is the exposure-referred SNR derived from first principles? (2) Is the output-referred SNR a special case of the exposure-referred SNR, or are they completely different? (3) How to compute the SNR efficiently? (4) What utilities can the SNR bring to solving imaging tasks? New theoretical results are derived for image sensors of any bit-depth and full-well capacity.

A 3D point cloud is typically constructed from depth measurements acquired by sensors at one or more viewpoints. The measurements suffer from both quantization and noise corruption. To improve quality, previous works denoise a point cloud \textit{a posteriori} after projecting the imperfect depth data onto 3D space. Instead, we enhance depth measurements directly on the sensed images \textit{a priori}, before synthesizing a 3D point cloud. By enhancing near the physical sensing process, we tailor our optimization to our depth formation model before subsequent processing steps that obscure measurement errors. Specifically, we model depth formation as a combined process of signal-dependent noise addition and non-uniform log-based quantization. The designed model is validated (with parameters fitted) using collected empirical data from a representative depth sensor. To enhance each pixel row in a depth image, we first encode intra-view similarities between available row pixels as edge weights via feature graph learning. We next establish inter-view similarities with another rectified depth image via viewpoint mapping and sparse linear interpolation. This leads to a maximum a posteriori (MAP) graph filtering objective that is convex and differentiable. We minimize the objective efficiently using accelerated gradient descent (AGD), where the optimal step size is approximated via Gershgorin circle theorem (GCT). Experiments show that our method significantly outperformed recent point cloud denoising schemes and state-of-the-art image denoising schemes in two established point cloud quality metrics., Comment: 16 pages,14 figures

Image deblurring in photon-limited conditions is ubiquitous in a variety of low-light applications such as photography, microscopy, and astronomy. However, the presence of photon shot noise due to low illumination and/or short exposure makes the deblurring task substantially more challenging than the conventional deblurring problems. In this paper, we present an algorithm unrolling approach for the photon-limited deblurring problem by unrolling a Plug-and-Play algorithm for a fixed number of iterations. By introducing a three-operator splitting formation of the Plug-and-Play framework, we obtain a series of differentiable steps which allows the fixed iteration unrolled network to be trained end-to-end. The proposed algorithm demonstrates significantly better image recovery compared to existing state-of-the-art deblurring approaches. We also present a new photon-limited deblurring dataset for evaluating the performance of algorithms., Comment: IEEE Transactions on Computational Imaging

Adversarial attacks pose a substantial threat to computer vision system security, but the social media industry constantly faces another form of "adversarial attack" in which the hackers attempt to upload inappropriate images and fool the automated screening systems by adding artificial graphics patterns. In this paper, we formulate the defense against such attacks as an artificial graphics pattern segmentation problem. We evaluate the efficacy of several segmentation algorithms and, based on observation of their performance, propose a new method tailored to this specific problem. Extensive experiments show that the proposed method outperforms the baselines and has a promising generalization capability, which is the most crucial aspect in segmenting artificial graphics patterns., Comment: ICCV 2021 Workshop on Adversarial Robustness in the Real World

We introduce OPtical ADversarial attack (OPAD). OPAD is an adversarial attack in the physical space aiming to fool image classifiers without physically touching the objects (e.g., moving or painting the objects). The principle of OPAD is to use structured illumination to alter the appearance of the target objects. The system consists of a low-cost projector, a camera, and a computer. The challenge of the problem is the non-linearity of the radiometric response of the projector and the spatially varying spectral response of the scene. Attacks generated in a conventional approach do not work in this setting unless they are calibrated to compensate for such a projector-camera model. The proposed solution incorporates the projector-camera model into the adversarial attack optimization, where a new attack formulation is derived. Experimental results prove the validity of the solution. It is demonstrated that OPAD can optically attack a real 3D object in the presence of background lighting for white-box, black-box, targeted, and untargeted attacks. Theoretical analysis is presented to quantify the fundamental performance limit of the system., Comment: ICCV Workshop 2021

Fast and accurate simulation of imaging through atmospheric turbulence is essential for developing turbulence mitigation algorithms. Recognizing the limitations of previous approaches, we introduce a new concept known as the phase-to-space (P2S) transform to significantly speed up the simulation. P2S is build upon three ideas: (1) reformulating the spatially varying convolution as a set of invariant convolutions with basis functions, (2) learning the basis function via the known turbulence statistics models, (3) implementing the P2S transform via a light-weight network that directly convert the phase representation to spatial representation. The new simulator offers 300x -- 1000x speed up compared to the mainstream split-step simulators while preserving the essential turbulence statistics., Comment: The paper will be published at the ICCV 2021

Graph signal processing is a ubiquitous task in many applications such as sensor, social, transportation and brain networks, point cloud processing, and graph neural networks. Often, graph signals are corrupted in the sensing process, thus requiring restoration. In this paper, we propose two graph signal restoration methods based on deep algorithm unrolling (DAU). First, we present a graph signal denoiser by unrolling iterations of the alternating direction method of multiplier (ADMM). We then suggest a general restoration method for linear degradation by unrolling iterations of Plug-and-Play ADMM (PnP-ADMM). In the second approach, the unrolled ADMM-based denoiser is incorporated as a submodule, leading to a nested DAU structure. The parameters in the proposed denoising/restoration methods are trainable in an end-to-end manner. Our approach is interpretable and keeps the number of parameters small since we only tune graph-independent regularization parameters. We overcome two main challenges in existing graph signal restoration methods: 1) limited performance of convex optimization algorithms due to fixed parameters which are often determined manually. 2) large number of parameters of graph neural networks that result in difficulty of training. Several experiments for graph signal denoising and interpolation are performed on synthetic and real-world data. The proposed methods show performance improvements over several existing techniques in terms of root mean squared error in both tasks.

Identification of high-risk driving situations is generally approached through collision risk estimation or accident pattern recognition. In this work, we approach the problem from the perspective of subjective risk. We operationalize subjective risk assessment by predicting driver behavior changes and identifying the cause of changes. To this end, we introduce a new task called driver-centric risk object identification (DROID), which uses egocentric video to identify object(s) influencing a driver's behavior, given only the driver's response as the supervision signal. We formulate the task as a cause-effect problem and present a novel two-stage DROID framework, taking inspiration from models of situation awareness and causal inference. A subset of data constructed from the Honda Research Institute Driving Dataset (HDD) is used to evaluate DROID. We demonstrate state-of-the-art DROID performance, even compared with strong baseline models using this dataset. Additionally, we conduct extensive ablative studies to justify our design choices. Moreover, we demonstrate the applicability of DROID for risk assessment., Comment: Submitted to TPAMI

Feature-based student-teacher learning, a training method that encourages the student's hidden features to mimic those of the teacher network, is empirically successful in transferring the knowledge from a pre-trained teacher network to the student network. Furthermore, recent empirical results demonstrate that, the teacher's features can boost the student network's generalization even when the student's input sample is corrupted by noise. However, there is a lack of theoretical insights into why and when this method of transferring knowledge can be successful between such heterogeneous tasks. We analyze this method theoretically using deep linear networks, and experimentally using nonlinear networks. We identify three vital factors to the success of the method: (1) whether the student is trained to zero training loss; (2) how knowledgeable the teacher is on the clean-input problem; (3) how the teacher decomposes its knowledge in its hidden features. Lack of proper control in any of the three factors leads to failure of the student-teacher learning method., Comment: Published at the Conference on Computer Vision and Pattern Recognition (CVPR 2021)

High dynamic range (HDR) imaging is one of the biggest achievements in modern photography. Traditional solutions to HDR imaging are designed for and applied to CMOS image sensors (CIS). However, the mainstream one-micron CIS cameras today generally have a high read noise and low frame-rate. These, in turn, limit the acquisition speed and quality, making the cameras slow in the HDR mode. In this paper, we propose a new computational photography technique for HDR imaging. Recognizing the limitations of CIS, we use the Quanta Image Sensor (QIS) to trade the spatial-temporal resolution with bit-depth. QIS is a single-photon image sensor that has comparable pixel pitch to CIS but substantially lower dark current and read noise. We provide a complete theoretical characterization of the sensor in the context of HDR imaging, by proving the fundamental limits in the dynamic range that QIS can offer and the trade-offs with noise and speed. In addition, we derive an optimal reconstruction algorithm for single-bit and multi-bit QIS. Our algorithm is theoretically optimal for \emph{all} linear reconstruction schemes based on exposure bracketing. Experimental results confirm the validity of the theory and algorithm, based on synthetic and real QIS data.

Imaging in low light is difficult because the number of photons arriving at the sensor is low. Imaging dynamic scenes in low-light environments is even more difficult because as the scene moves, pixels in adjacent frames need to be aligned before they can be denoised. Conventional CMOS image sensors (CIS) are at a particular disadvantage in dynamic low-light settings because the exposure cannot be too short lest the read noise overwhelms the signal. We propose a solution using Quanta Image Sensors (QIS) and present a new image reconstruction algorithm. QIS are single-photon image sensors with photon counting capabilities. Studies over the past decade have confirmed the effectiveness of QIS for low-light imaging but reconstruction algorithms for dynamic scenes in low light remain an open problem. We fill the gap by proposing a student-teacher training protocol that transfers knowledge from a motion teacher and a denoising teacher to a student network. We show that dynamic scenes can be reconstructed from a burst of frames at a photon level of 1 photon per pixel per frame. Experimental results confirm the advantages of the proposed method compared to existing methods., Comment: Published in the 16th European Conference on Computer Vision (ECCV) 2020

State-of-the-art image classifiers are trained and tested using well-illuminated images. These images are typically captured by CMOS image sensors with at least tens of photons per pixel. However, in dark environments when the photon flux is low, image classification becomes difficult because the measured signal is suppressed by noise. In this paper, we present a new low-light image classification solution using Quanta Image Sensors (QIS). QIS are a new type of image sensors that possess photon counting ability without compromising on pixel size and spatial resolution. Numerous studies over the past decade have demonstrated the feasibility of QIS for low-light imaging, but their usage for image classification has not been studied. This paper fills the gap by presenting a student-teacher learning scheme which allows us to classify the noisy QIS raw data. We show that with student-teacher learning, we are able to achieve image classification at a photon level of one photon per pixel or lower. Experimental results verify the effectiveness of the proposed method compared to existing solutions., Comment: Published in the 16th European Conference on Computer Vision (ECCV) 2020

When training an estimator such as a neural network for tasks like image denoising, it is often preferred to train one estimator and apply it to all noise levels. The de facto training protocol to achieve this goal is to train the estimator with noisy samples whose noise levels are uniformly distributed across the range of interest. However, why should we allocate the samples uniformly? Can we have more training samples that are less noisy, and fewer samples that are more noisy? What is the optimal distribution? How do we obtain such a distribution? The goal of this paper is to address this training sample distribution problem from a minimax risk optimization perspective. We derive a dual ascent algorithm to determine the optimal sampling distribution of which the convergence is guaranteed as long as the set of admissible estimators is closed and convex. For estimators with non-convex admissible sets such as deep neural networks, our dual formulation converges to a solution of the convex relaxation. We discuss how the algorithm can be implemented in practice. We evaluate the algorithm on linear estimators and deep networks., Comment: Published in the 37th International Conference on Machine Learning (ICML) 2020

Simulating atmospheric turbulence is an essential task for evaluating turbulence mitigation algorithms and training learning-based methods. Advanced numerical simulators for atmospheric turbulence are available, but they require evaluating wave propagation which is computationally expensive. In this paper, we present a propagation-free method for simulating imaging through turbulence. The key idea behind our work is a new method to draw inter-modal and spatially correlated Zernike coefficients. By establishing the equivalence between the angle-of-arrival correlation by Basu, McCrae and Fiorino (2015) and the multi-aperture correlation by Chanan (1992), we show that the Zernike coefficients can be drawn according to a covariance matrix defining the correlations. We propose fast and scalable sampling strategies to draw these samples. The new method allows us to compress the wave propagation problem into a sampling problem, hence making the new simulator significantly faster than existing ones. Experimental results show that the simulator has an excellent match with the theory and real turbulence data.

A significant amount of people die in road accidents due to driver errors. To reduce fatalities, developing intelligent driving systems assisting drivers to identify potential risks is in an urgent need. Risky situations are generally defined based on collision prediction in the existing works. However, collision is only a source of potential risks, and a more generic definition is required. In this work, we propose a novel driver-centric definition of risk, i.e., objects influencing drivers' behavior are risky. A new task called risk object identification is introduced. We formulate the task as the cause-effect problem and present a novel two-stage risk object identification framework based on causal inference with the proposed object-level manipulable driving model. We demonstrate favorable performance on risk object identification compared with strong baselines on the Honda Research Institute Driving Dataset (HDD). Our framework achieves a substantial average performance boost over a strong baseline by 7.5%., Comment: Accepted to the International Conference on Intelligent Robots and Systems (IROS) 2020

To enable intelligent automated driving systems, a promising strategy is to understand how human drives and interacts with road users in complicated driving situations. In this paper, we propose a 3D-aware egocentric spatial-temporal interaction framework for automated driving applications. Graph convolution networks (GCN) is devised for interaction modeling. We introduce three novel concepts into GCN. First, we decompose egocentric interactions into ego-thing and ego-stuff interaction, modeled by two GCNs. In both GCNs, ego nodes are introduced to encode the interaction between thing objects (e.g., car and pedestrian), and interaction between stuff objects (e.g., lane marking and traffic light). Second, objects' 3D locations are explicitly incorporated into GCN to better model egocentric interactions. Third, to implement ego-stuff interaction in GCN, we propose a MaskAlign operation to extract features for irregular objects. We validate the proposed framework on tactical driver behavior recognition. Extensive experiments are conducted using Honda Research Institute Driving Dataset, the largest dataset with diverse tactical driver behavior annotations. Our framework demonstrates substantial performance boost over baselines on the two experimental settings by 3.9% and 6.0%, respectively. Furthermore, we visualize the learned affinity matrices, which encode ego-thing and ego-stuff interactions, to showcase the proposed framework can capture interactions effectively., Comment: Accepted to the International Conference on Robotics and Automation (ICRA) 2020

State-of-the-art atmospheric turbulence image restoration methods utilize standard image processing tools such as optical flow, lucky region and blind deconvolution to restore the images. While promising results have been reported over the past decade, many of the methods are agnostic to the physical model that generates the distortion. In this paper, we revisit the turbulence restoration problem by analyzing the reference frame generation and the blind deconvolution steps in a typical restoration pipeline. By leveraging tools in large deviation theory, we rigorously prove the minimum number of frames required to generate a reliable reference for both static and dynamic scenes. We discuss how a turbulence agnostic model can lead to potential flaws, and how to configure a simple spatial-temporal non-local weighted averaging method to generate references. For blind deconvolution, we present a new data-driven prior by analyzing the distributions of the point spread functions. We demonstrate how a simple prior can outperform state-of-the-art blind deconvolution methods.

Quanta image sensor (QIS) is envisioned to be the next generation image sensor after CCD and CMOS. In this paper, we discuss how to design color filter arrays for QIS and other small pixels. Designing color filter arrays for small pixels is challenging because maximizing the light efficiency while suppressing aliasing and crosstalk are conflicting tasks. We present an optimization-based framework which unifies several mainstream color filter array design methodologies. Our method offers greater generality and flexibility. Compared to existing methods, the new framework can simultaneously handle luminance sensitivity, chrominance sensitivity, cross-talk, anti-aliasing, manufacturability and orthogonality. Extensive experimental comparisons demonstrate the effectiveness of the framework.

The Plug-and-Play (PnP) ADMM algorithm is a powerful image restoration framework that allows advanced image denoising priors to be integrated into physical forward models to generate high quality image restoration results. However, despite the enormous number of applications and several theoretical studies trying to prove the convergence by leveraging tools in convex analysis, very little is known about why the algorithm is doing so well. The goal of this paper is to fill the gap by discussing the performance of PnP ADMM. By restricting the denoisers to the class of graph filters under a linearity assumption, or more specifically the symmetric smoothing filters, we offer three contributions: (1) We show conditions under which an equivalent maximum-a-posteriori (MAP) optimization exists, (2) we present a geometric interpretation and show that the performance gain is due to an intrinsic pre-denoising characteristic of the PnP prior, (3) we introduce a new analysis technique via the concept of consensus equilibrium, and provide interpretations to problems involving multiple priors.

Extracting accurate foreground objects from a scene is an essential step for many video applications. Traditional background subtraction algorithms can generate coarse estimates, but generating high quality masks requires professional softwares with significant human interventions, e.g., providing trimaps or labeling key frames. We propose an automatic foreground extraction method in applications where a static but imperfect background is available. Examples include filming and surveillance where the background can be captured before the objects enter the scene or after they leave the scene. Our proposed method is very robust and produces significantly better estimates than state-of-the-art background subtraction, video segmentation and alpha matting methods. The key innovation of our method is a novel information fusion technique. The fusion framework allows us to integrate the individual strengths of alpha matting, background subtraction and image denoising to produce an overall better estimate. Such integration is particularly important when handling complex scenes with imperfect background. We show how the framework is developed, and how the individual components are built. Extensive experiments and ablation studies are conducted to evaluate the proposed method.

Given a set of image denoisers, each having a different denoising capability, is there a provably optimal way of combining these denoisers to produce an overall better result? An answer to this question is fundamental to designing an ensemble of weak estimators for complex scenes. In this paper, we present an optimal combination scheme by leveraging deep neural networks and convex optimization. The proposed framework, called the Consensus Neural Network (CsNet), introduces three new concepts in image denoising: (1) A provably optimal procedure to combine the denoised outputs via convex optimization; (2) A deep neural network to estimate the mean squared error (MSE) of denoised images without needing the ground truths; (3) An image boosting procedure using a deep neural network to improve contrast and to recover lost details of the combined images. Experimental results show that CsNet can consistently improve denoising performance for both deterministic and neural network denoisers., Comment: IEEE Transaction on Image Processing

Regularized inversion methods for image reconstruction are used widely due to their tractability and ability to combine complex physical sensor models with useful regularity criteria. Such methods motivated the recently developed Plug-and-Play prior method, which provides a framework to use advanced denoising algorithms as regularizers in inversion. However, the need to formulate regularized inversion as the solution to an optimization problem limits the possible regularity conditions and physical sensor models. In this paper, we introduce Consensus Equilibrium (CE), which generalizes regularized inversion to include a much wider variety of both forward components and prior components without the need for either to be expressed with a cost function. CE is based on the solution of a set of equilibrium equations that balance data fit and regularity. In this framework, the problem of MAP estimation in regularized inversion is replaced by the problem of solving these equilibrium equations, which can be approached in multiple ways. The key contribution of CE is to provide a novel framework for fusing multiple heterogeneous models of physical sensors or models learned from data. We describe the derivation of the CE equations and prove that the solution of the CE equations generalizes the standard MAP estimate under appropriate circumstances. We also discuss algorithms for solving the CE equations, including ADMM with a novel form of preconditioning and Newton's method. We give examples to illustrate consensus equilibrium and the convergence properties of these algorithms and demonstrate this method on some toy problems and on a denoising example in which we use an array of convolutional neural network denoisers, none of which is tuned to match the noise level in a noisy image but which in consensus can achieve a better result than any of them individually., Comment: 17 pages

Quanta Image Sensor (QIS) is a binary imaging device envisioned to be the next generation image sensor after CCD and CMOS. Equipped with a massive number of single photon detectors, the sensor has a threshold $q$ above which the number of arriving photons will trigger a binary response "1", or "0" otherwise. Existing methods in the device literature typically assume that $q=1$ uniformly. We argue that a spatially varying threshold can significantly improve the signal-to-noise ratio of the reconstructed image. In this paper, we present an optimal threshold design framework. We make two contributions. First, we derive a set of oracle results to theoretically inform the maximally achievable performance. We show that the oracle threshold should match exactly with the underlying pixel intensity. Second, we show that around the oracle threshold there exists a set of thresholds that give asymptotically unbiased reconstructions. The asymptotic unbiasedness has a phase transition behavior which allows us to develop a practical threshold update scheme using a bisection method. Experimentally, the new threshold design method achieves better rate of convergence than existing methods., Comment: 12 pages main paper, and 8 pages supplementary

Alternating direction method of multiplier (ADMM) is a widely used algorithm for solving constrained optimization problems in image restoration. Among many useful features, one critical feature of the ADMM algorithm is its modular structure which allows one to plug in any off-the-shelf image denoising algorithm for a subproblem in the ADMM algorithm. Because of the plug-in nature, this type of ADMM algorithms is coined the name "Plug-and-Play ADMM". Plug-and-Play ADMM has demonstrated promising empirical results in a number of recent papers. However, it is unclear under what conditions and by using what denoising algorithms would it guarantee convergence. Also, since Plug-and-Play ADMM uses a specific way to split the variables, it is unclear if fast implementation can be made for common Gaussian and Poissonian image restoration problems. In this paper, we propose a Plug-and-Play ADMM algorithm with provable fixed point convergence. We show that for any denoising algorithm satisfying an asymptotic criteria, called bounded denoisers, Plug-and-Play ADMM converges to a fixed point under a continuation scheme. We also present fast implementations for two image restoration problems on super-resolution and single-photon imaging. We compare Plug-and-Play ADMM with state-of-the-art algorithms in each problem type, and demonstrate promising experimental results of the algorithm., Comment: 14 pages

This paper studies a type of image priors that are constructed implicitly through the alternating direction method of multiplier (ADMM) algorithm, called the algorithm-induced prior. Different from classical image priors which are defined before running the reconstruction algorithm, algorithm-induced priors are defined by the denoising procedure used to replace one of the two modules in the ADMM algorithm. Since such prior is not explicitly defined, analyzing the performance has been difficult in the past. Focusing on the class of symmetric smoothing filters, this paper presents an explicit expression of the prior induced by the ADMM algorithm. The new prior is reminiscent to the conventional graph Laplacian but with stronger reconstruction performance. It can also be shown that the overall reconstruction has an efficient closed-form implementation if the associated symmetric smoothing filter is low rank. The results are validated with experiments on image inpainting.