Photon-Limited Imaging

What Does a One-Bit Quanta Image Sensor Offer?

IEEE Transactions on Computational Imaging, 2022
Stanley H. Chan

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.

Review of Quanta Image Sensors

IEEE Journal of Electron Devices, 2022
Jiaju Ma, Stanley H. Chan, Eric R. Fossum

The quanta image sensor (QIS) is a photon-counting image sensor that has been implemented using different electron devices, including impact ionization-gain devices, such as the single-photon avalanche detectors (SPADs), and low-capacitance, high conversion-gain devices, such as modified CMOS image sensors (CIS) with deep subelectron read noise and/or low noise readout signal chains. This article primarily focuses on CIS QIS, but recent progress of both types is addressed. Signal processing progress, such as denoising, critical to improving apparent signal-to-noise ratio, is also reviewed as an enabling coinnovation.

Photon-Limited Blind Deconvolution using Unsupervised Iterative Kernel Estimation

Yash Sanghvi, Abhiram Gnanasambandam, Zhiyuan Mao, Stanley H. Chan

Blind deconvolution in low-light is one of the more challenging problems in image restoration because of the photon shot noise. However, existing algorithms – both classical and deep-learning based – are not designed for this condition. When the shot noise is strong, conventional deconvolution methods fail because (1) the presence of noise makes the estimation of the blur kernel difficult; (2) generic deep-restoration models rarely model the forward process explicitly; (3) there are currently no iterative strategies to incorporate a non-blind solver in a kernel estimation stage. This paper addresses these challenges by presenting an 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.

Photon-Limited Non-Blind Deblurring Using Algorithm Unrolling

Yash Sanghvi, Abhiram Gnanasambandam, Stanley H. Chan
Project Page:

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.

Exposure referred Signal-to-Noise Ratio for Digital Image Sensors

IEEE Transactions on Computational Imaging, 2022
Abhiram Gnanasambandam and Stanley H. Chan

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.

Electronic Imaging 2022 Short Course

Signal Processing for Photon-Limited Imaging
Stanley Chan

Photon-Limited Object Detection using Non-local Feature Matching and Knowledge Distillation

IEEE International Conference on Computer Vision Workshop, 2021
Chengxi Li, Xiangyu Qu, Abhiram Gnanasambandam, Omar A. Elgendy, Jiaju Ma, Stanley H. Chan

Robust object detection under photon-limited conditions is crucial for applications such as night vision, surveillance, and microscopy, where the number of photons per pixel is low due to a dark environment and/or a short integration time. While the mainstream “low-light” image enhancement methods have produced promising results that improve the image contrast between the foreground and background through advanced coloring techniques, the more challenging problem of mitigating the photon shot noise inherited from the random Poisson process remains open. In this paper, we present a photon-limited object detection framework by adding two ideas to state-of-the-art object detectors: 1) a space-time non-local module that leverages the spatial-temporal information across an image sequence in the feature space, and 2) knowledge distillation in the form of student-teacher learning to improve the robustness of the detector’s feature extractor against noise. Experiments are conducted to demonstrate the improved performance of the proposed method in comparison with state-of-the-art baselines. When integrated with the latest photon counting devices, the algorithm achieves more than 50% mean average precision at a photon level of 1 photon per pixel.

Low-Light Demosaicking and Denoising for Small Pixels Using Learned Frequency Selection

IEEE Transactions on Computational Imaging, 2021
Omar Elgendy, Abhiram Gnanasambandam, Stanley H. Chan, and Jiaju Ma

Low-light imaging is a challenging task because of the excessive photon shot noise. Color imaging in low-light is even more difficult because one needs to demosaick and denoise simultaneously. Existing demosaicking algorithms are mostly designed for well-illuminated scenarios, which fail to work with low-light. Recognizing the recent development of small pixels and low read noise image sensors, we propose a learning-based joint demosaicking and denoising algorithm for low-light color imaging. Our method combines the classical theory of color filter arrays and modern deep learning. We use an explicit carrier to demodulate the color from the input Bayer pattern image. We integrate trainable filters into the demodulation scheme to improve flexibility. We introduce a guided filtering module to transfer knowledge from the luma channel to the chroma channels, thus offering substantially more reliable denoising. Extensive experiments are performed to evaluate the performance of the proposed method, using both synthetic datasets and real data. Results indicate that the proposed method offers consistently better performance over the current state-of-the-art, across several standard evaluation metrics.

HDR Imaging with Quanta Image Sensors: Theoretical Limits and Optimal Reconstruction

IEEE Transactions on Computational Imaging, 2020
Abhiram Gnanasambandam and Stanley H. Chan

An earlier version of the paper is presented at International Image Sensor Workshop (IISW) 2019.
Manuscript: PDF

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.

Dynamic Low-light Imaging with Quanta Image Sensors

European Conference on Computer Vision (ECCV), 2020.
Yiheng Chi, Abhiram Gnanasambandam, Vladlen Koltun, and Stanley H. Chan

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.

Image Classification in the Dark using Quanta Image Sensors

European Conference on Computer Vision (ECCV), 2020
Abhiram Gnanasambandam, and Stanley H. Chan

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.

Color Filter Arrays Design for Quanta Image Sensors

IEEE Trans. Computational Imaging, 2019.
Omar A. Elgendy, and Stanley H. Chan

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. Designing color filter arrays for small pixels such as QIS 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 and 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 and generality of the framework.

Megapixel photon-counting color imaging using quanta image sensor

OSA Optics Express 2019
Abhiram Gnanasambandam, Omar A. Elgendy, Jiaju Ma, and Stanley H. Chan

Quanta Image Sensor (QIS) is a single-photon detector designed for extremely low light imaging conditions. Majority of the existing QIS prototypes are monochrome based on single-photon avalanche diodes (SPAD). Passive color imaging has not been demonstrated with single-photon detectors due to the intrinsic difficulty of shrinking the pixel size and increasing the spatial resolution while maintaining acceptable intra-pixel cross-talk. In this paper, we present image reconstruction of the first color QIS with a resolution of 1024-by-1024 pixels, supporting both single-bit and multi-bit photon counting capability. Our color image reconstruction is enabled by a customized joint demosaicing-denoising algorithm, leveraging truncated Poisson statistics and variance stabilizing transforms. Experimental results of the new sensor and algorithm demonstrate superior color imaging performance for very low-light conditions with a mean exposure of as low as a few photons per pixel in both real and simulated images.

Photon-counting Imaging with Multi-bit Quanta Image Sensors

International Image Sensor Workshop (IISW), 2019
Manuscript: PDF
Jiaju Ma, Yu-Wing Chung, Abhiram Gnanasambandam, Stanley H. Chan, and Saleh Masoodian

Image Reconstruction for Quanta Image Sensors using Deep Neural Networks

Manuscript: PDF
Joon Hee Choi, Omar A. Elgendy and Stanley H. Chan

Quanta Image Sensor (QIS) is a single-photon image sensor that oversamples the light field to generate binary measurements. Its single-photon sensitivity makes it an ideal candidate for the next generation image sensor after CMOS. However, image reconstruction of the sensor remains a challenging issue. Existing image reconstruction algorithms are largely based on optimization. In this paper, we present the first deep neural network approach for QIS image reconstruction. Our deep neural network takes the binary bit stream of QIS as input, learns the nonlinear transformation and denoising simultaneously. Experimental results show that the proposed network produces significantly better reconstruction results compared to existing methods.

Optimal Threshold Design for Quanta Image Sensors

(ICIP 2016 Best Paper Award)

IEEE Trans. Computational Imaging, 2018
Omar A. Elgendy and Stanley H. Chan

Also presented in IEEE ICIP 2016
Manuscript: PDF

MATLAB Implementation (1.1MB)

Quanta Image Sensor (QIS) has been envisioned as a candidate solution for next generation image sensors. We provide two new contributions to the signal processing aspects of QIS. First, we develop an image reconstruction algorithm to recover the underlying images from the QIS data, which is a massive array of binarized Poisson random variables. The new algorithm supersedes existing methods by enabling arbitrary threshold level. Second, we present a threshold design scheme to adaptively update the threshold level for optimal image reconstruction. We discuss the existence of a phase transition in determining the optimal threshold. Experimental results on tone-mapped high dynamic range images validates the effectiveness of the threshold scheme and the image reconstruction algorithm.

Non-Iterative Image Reconstruction


Quanta image sensor (QIS) is a class of single photon imaging devices that measure light intensity using oversampled binary observations. Because of the stochastic nature of the photon arrivals, data acquired by QIS is a massive stream of random binary bits. The goal of image reconstruction is to recover the underlying image from these bits. In this paper, we present a non-iterative image reconstruction algorithm for QIS. Unlike existing reconstruction methods that formulate the problem from an optimization perspective, the new algorithm directly recovers the images through a pair of nonlinear transformations and an off-the-shelf image denoising algorithm. By skipping the usual optimization procedure, we achieve orders of magnitude improvement in speed and even better image reconstruction quality. We validate the new algorithm on synthetic datasets as well as real videos collected by 1-bit SPAD cameras.


  1. Stanley H. Chan, Omar Elgendy and Xiran Wang, ‘‘Images from bits: Non-iterative image reconstruction for quanta image sensors’’, MDPI Sensors Special Issue on Photon-Counting Image Sensors, vol. 16, no. 11, paper 1961, pp.1-21, Nov. 2016.


ADMM Image Reconstruction


Recent advances in materials, devices and fabrication technologies have motivated a strong momentum in developing solid-state sensors that can detect individual photons in space and time. It has been envisioned that such sensors can eventually achieve very high spatial resolutions as well as high frame rates. In this paper, we present an efficient algorithm to reconstruct images from the massive binary bit-streams generated by these sensors. Based on the concept of alternating direction method of multipliers (ADMM), we transform the computationally intensive optimization problem into a sequence of subproblems, each of which has efficient implementations in the form of polyphase-domain filtering or pixel-wise nonlinear mappings. Moreover, we reformulate the original maximum likelihood estimation as maximum a posterior estimation by introducing a total variation prior. Numerical results demonstrate the strong performance of the proposed method, which achieves several dB's of improvement in PSNR and requires a shorter runtime as compared to standard gradient-based approaches.


  1. Stanley H. Chan, and Yue M. Lu, ‘‘Efficient image reconstruction for giga-pixel quanta image sensors’’, IEEE GlobalSIP, pp. 312-316, Altanta, Georgia, Dec. 2014,