Recent advances in photographic sensing technologies have made it possible to achieve light detection in terms of a single photon. Photon counting sensors are being increasingly used in many diverse applications. We address the problem of jointly recovering spatial and temporal scene radiance from very few photon counts. Our ConvNet-based scheme effectively combines spatial and temporal information present in measurements to reduce noise. We demonstrate that using our method one can acquire videos at a high frame rate and still achieve good quality signal-to-noise ratio. Experiments show that the proposed scheme performs quite well in different challenging scenarios while the existing approaches are unable to handle them.
Recent works in range imaging through SPAD sensors include @cite_35 @cite_30 @cite_7 . SPAD cameras have been used to perform challenging tasks such as transient imaging @cite_33 @cite_13 @cite_38 @cite_31 @cite_39 , non-line-of sight imaging @cite_40 @cite_22 @cite_28 @cite_27 and imaging through fog @cite_15 . Closely related to the topic of single photon counting is that of Binary Quanta image sensors @cite_11 @cite_37 . These sensors were developed with the objective of shrinking the pixel pitch. In Quanta imaging, the densely defined sensors oversample the scene radiance to generate binary measurements @cite_11 @cite_3 . Image reconstruction schemes have been proposed for these sensors @cite_46 @cite_1 @cite_23 @cite_21 . The main difference between these reconstruction methods and our scheme is that these algorithms consider the availability of a higher number of samples to predict the image intensity at a pixel location. These methods have mainly focused on recovering a static image. In contrast, our focus is on recovering videos.
@cite_30 @cite_35 @cite_22 @cite_3 @cite_15 @cite_38 @cite_21 @cite_39 @cite_23 @cite_46 @cite_37 @cite_7 @cite_28 @cite_40 @cite_27 @cite_33 @cite_1 @cite_31 @cite_13 @cite_11
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Single-photon avalanche diode (SPAD) based transient imaging suffers from an aberration called pile-up. When multiple photons arrive within a single repetition period of the illuminating laser, the SPAD records only the arrival of the first photon; this leads to a bias in the recorded light transient wherein the transient response at later time-instants are under-estimated. An unfortunate consequence of this is the need to operate the illumination at low-power levels to reduce the probability of multiple photons returning in a single period. Operating the laser at low power results in either low signal-to-noise ratio (SNR) in the measured transients or reduced frame rate due to longer exposure durations to achieve a high SNR. In this paper, we propose a signal processing-based approach to compensate pile-up in post-processing, thereby enabling high power operation of the illuminating laser. While increasing illumination does cause a fundamental information loss in the data captured by SPAD, we quantify this information loss using Cramer-Rao bound and show that the errors in our framework are only limited to this information loss. We experimentally validate our hypotheses using real data from a lab prototype. In this paper, we present a novel technique, based on compressive sensing principles, for reconstruction and enhancement of multi-dimensional image data. Our method is a major improvement and generalization of the multi-scale sparsity based tomographic denoising (MSBTD) algorithm we recently introduced for reducing speckle noise. Our new technique exhibits several advantages over MSBTD, including its capability to simultaneously reduce noise and interpolate missing data. Unlike MSBTD, our new method does not require an a priori high-quality image from the target imaging subject and thus offers the potential to shorten clinical imaging sessions. This novel image restoration method, which we termed sparsity based simultaneous denoising and interpolation (SBSDI), utilizes sparse representation dictionaries constructed from previously collected datasets. We tested the SBSDI algorithm on retinal spectral domain optical coherence tomography images captured in the clinic. Experiments showed that the SBSDI algorithm qualitatively and quantitatively outperforms other state-of-the-art methods. The development of multisensor systems in recent years has led to great increase in the amount of available remote sensing data. Image fusion techniques aim at inferring high quality images of a given area from degraded versions of the same area obtained by multiple sensors. This paper focuses on pansharpening, which is the inference of a high spatial resolution multispectral image from two degraded versions with complementary spectral and spatial resolution characteristics: 1) a low spatial resolution multispectral image and 2) a high spatial resolution panchromatic image. We introduce a new variational model based on spatial and spectral sparsity priors for the fusion. In the spectral domain, we encourage low-rank structure, whereas in the spatial domain, we promote sparsity on the local differences. Given the fact that both panchromatic and multispectral images are integrations of the underlying continuous spectra using different channel responses, we propose to exploit appropriate regularizations based on both spatial and spectral links between panchromatic and fused multispectral images. A weighted version of the vector total variation norm of the data matrix is employed to align the spatial information of the fused image with that of the panchromatic image. With regard to spectral information, two different types of regularization are proposed to promote a soft constraint on the linear dependence between the panchromatic and fused multispectral images. The first one estimates directly the linear coefficients from the observed panchromatic and low-resolution multispectral images by linear regression while the second one employs the principal component pursuit to obtain a robust recovery of the underlying low-rank structure. We also show that the two regularizers are strongly related. The basic idea of both regularizers is that the fused image should have low-rank and preserve edge locations. We use a variation of the recently proposed split augmented Lagrangian shrinkage algorithm to effectively solve the proposed variational formulations. Experimental results on simulated and real remote sensing images show the effectiveness of the proposed pansharpening method compared with the state-of-the-art. Over the last decade, several techniques have been developed for looking around the corner by exploiting the round-trip travel time of photons. Typically, these techniques necessitate the collection of a large number of measurements with varying virtual source and virtual detector locations. This data is then processed by a reconstruction algorithm to estimate the hidden scene. As a consequence, even when the region of interest in the hidden volume is small and limited, the acquisition time needed is large as the entire dataset has to be acquired and then processed.In this paper, we present the first example of scanning based non-line-of-sight imaging technique. The key idea is that if the virtual sources (pulsed sources) on the wall are delayed using a quadratic delay profile (much like the quadratic phase of a focusing lens), then these pulses arrive at the same instant at a single point in the hidden volume – the point being scanned. On the imaging side, applying quadratic delays to the virtual detectors before integration on a single gated detector allows us to ‘focus’ and scan each point in the hidden volume. By changing the quadratic delay profiles, we can focus light at different points in the hidden volume. This provides the first example of scanning based non-line-of-sight imaging, allowing us to focus our measurements only in the region of interest. We derive the theoretical underpinnings of ‘temporal focusing’, show compelling simulations of performance analysis, build a hardware prototype system and demonstrate real results. Imaging through fog has important applications in industries such as self-driving cars, augmented driving, airplanes, helicopters, drones and trains. Here we show that time profiles of light reflected from fog have a distribution (Gamma) that is different from light reflected from objects occluded by fog (Gaussian). This helps to distinguish between background photons reflected from the fog and signal photons reflected from the occluded object. Based on this observation, we recover reflectance and depth of a scene obstructed by dense, dynamic, and heterogeneous fog. For practical use cases, the imaging system is designed in optical reflection mode with minimal footprint and is based on LIDAR hardware. Specifically, we use a single photon avalanche diode (SPAD) camera that time-tags individual detected photons. A probabilistic computational framework is developed to estimate the fog properties from the measurement itself, without prior knowledge. Other solutions are based on radar that suffers from poor resolution (due to the long wavelength), or on time gating that suffers from low signal-to-noise ratio. The suggested technique is experimentally evaluated in a wide range of fog densities created in a fog chamber It demonstrates recovering objects 57cm away from the camera when the visibility is 37cm. In that case it recovers depth with a resolution of 5cm and scene reflectance with an improvement of 4dB in PSNR and 3.4x reconstruction quality in SSIM over time gating techniques. The pursuit of smaller pixel sizes at ever increasing resolution in digital image sensors is mainly driven by the stringent price and form-factor requirements of sensors and optics in the cellular phone market. Recently, Eric Fossum proposed a novel concept of an image sensor with dense sub-diffraction limit one-bit pixels (jots), which can be considered a digital emulation of silver halide photographic film. This idea has been recently embodied as the EPFL Gigavision camera. A major bottleneck in the design of such sensors is the image reconstruction process, producing a continuous high dynamic range image from oversampled binary measurements. The extreme quantization of the Poisson statistics is incompatible with the assumptions of most standard image processing and enhancement frameworks. The recently proposed maximum-likelihood (ML) approach addresses this difficulty, but suffers from image artefacts and has impractically high computational complexity. In this work, we study a variant of a sensor with binary threshold pixels and propose a reconstruction algorithm combining an ML data fitting term with a sparse synthesis prior. We also show an efficient hardware-friendly real-time approximation of this inverse operator. Promising results are shown on synthetic data as well as on HDR data emulated using multiple exposures of a regular CMOS sensor. Recent development of compressive sensing has greatly benefited radar imaging problems. In this paper, we investigate the problem of obtaining enhanced targets such as ships and airplanes, where targets often exhibit structured sparsity. A novel structured sparsity-driven autofocus algorithm is proposed based on sparse Bayesian framework.The structured sparse prior is imposed on the target scene in a statistical manner. Based on a statistical framework, the proposed algorithm can simultaneously cope with structured sparse recovery and phase error correction problem. The focused high-resolution radar image can be obtained by iteratively estimating scattering coefficients and phase. Due to the structured sparse constraint, the proposed algorithm can desirably preserve the target region and alleviate over-shrinkage problem, compared to previous sparsity-driven auto-focus approaches.Moreover, to accelerate convergence rate of the algorithm, we propose to adaptively eliminate noise-only range cells in estimating phase errors. The selection is conveniently conducted based on the parameters controlling sparsity degree of the signal in the proposed hierarchical model.The simulated and real data experimental results demonstrate that the proposed algorithm can obtain more concentrated images with much smaller number of iterations, particularly in low SNR and highly under-sampling scenarios. HighlightsA novel structured sparsity-driven autofocus algorithm is proposed based on sparse Bayesian framework.To accelerate convergence rate of the algorithm, we propose to adaptively eliminate noise-only range cells in phase error estimation stage.The proposed algorithm can obtain more concentrated images with much smaller number of iterations, particularly in low SNR and highly under-sampling scenarios. While high resolution, regularly gridded observations are generally preferred in remote sensing, actual observations are often not evenly sampled and have lower-than-desired resolution. Hence, there is an interest in resolution enhancement and image reconstruction. This paper discusses a general theory and techniques for image reconstruction and creating enhanced resolution images from irregularly sampled data. Using irregular sampling theory, we consider how the frequency content in aperture function-attenuated sidelobes can be recovered from oversampled data using reconstruction techniques, thus taking advantage of the high frequency content of measurements made with nonideal aperture filters. We show that with minor modification, the algebraic reconstruction technique (ART) is functionally equivalent to Grochenig's (1992) irregular sampling reconstruction algorithm. Using simple Monte Carlo simulations, we compare and contrast the performance of additive ART, multiplicative ART, and the scatterometer image reconstruction (SIR) (a derivative of multiplicative ART) algorithms with and without noise. The reconstruction theory and techniques have applications with a variety of sensors and can enable enhanced resolution image production from many nonimaging sensors. The technique is illustrated with ERS-2 and SeaWinds scatterometer data. Time-of-flight depth imaging and transient imaging are two imaging modalities that have recently received a lot of interest. Despite much research, existing hardware systems are limited either in terms of temporal resolution or are prohibitively expensive. Arrays of Single Photon Avalanche Diodes (SPADs) promise to fill this gap by providing higher temporal resolution at an affordable cost. Unfortunately SPAD arrays are to date only available in relatively small resolutions. In this work we aim to overcome the spatial resolution limit of SPAD arrays by employing a compressive sensing camera design. Using a DMD and custom optics, we achieve an image resolution of up to 800A—400 on SPAD Arrays of resolution 64A—32. Using our new data fitting model for the time histograms, we suppress the noise while abstracting the phase and amplitude information, so as to realize a temporal resolution of a few tens of picoseconds. We describe an imaging architecture for compressive video sensing termed programmable pixel compressive camera (P2C2). P2C2 allows us to capture fast phenomena at frame rates higher than the camera sensor. In P2C2, each pixel has an independent shutter that is modulated at a rate higher than the camera frame-rate. The observed intensity at a pixel is an integration of the incoming light modulated by its specific shutter. We propose a reconstruction algorithm that uses the data from P2C2 along with additional priors about videos to perform temporal super-resolution. We model the spatial redundancy of videos using sparse representations and the temporal redundancy using brightness constancy constraints inferred via optical flow. We show that by modeling such spatio-temporal redundancies in a video volume, one can faithfully recover the underlying high-speed video frames from the observed low speed coded video. The imaging architecture and the reconstruction algorithm allows us to achieve temporal super-resolution without loss in spatial resolution. We implement a prototype of P2C2 using an LCOS modulator and recover several videos at 200 fps using a 25 fps camera. Distributed sampling and reconstruction of a physical field using an array of sensors is a problem of considerable interest in environmental monitoring applications of sensor networks. Our recent work has focused on the sampling of bandlimited sensor fields. However, sensor fields are not perfectly bandlimited but typically have rapidly decaying spectra. In a classical sampling set-up it is possible to precede the A D sampling operation with an appropriate analog anti-aliasing filter. However, in the case of sensor networks, this is infeasible since sampling must precede filtering. We show that even though the effects of aliasing on the reconstruction cannot be prevented due to the "filter-less" sampling constraint, they can be suitably controlled by oversampling and carefully reconstructing the field from the samples. We show using a dither-based scheme that it is possible to estimate non-bandlimited fields with a precision that depends on how fast the spectral content of the field decays. We develop a framework for analyzing non-bandlimited fields that lead to upper bounds on the maximum pointwise error for a spatial bit rate of R bits meter. We present results for fields with exponentially decaying spectra as an illustration. In particular, we show that for fields f(t) with exponential tails; i.e., F( spl omega ) < spl pi spl alpha sup - spl alpha | spl omega | , the maximum pointwise error decays as c2e sup -a sub 1 spl radic R+ c3 1 spl radic R (e sup -2a sub 1 spl radic R) with spatial bit rate R bits meter. Finally, we show that for fields with spectra that have a finite second moment, the distortion decreases as O((1 N) sup 2 3 ) as the density of sensors, N, scales up to infinity . We show that if D is the targeted non-zero distortion, then the required (finite) rate R scales as O (1 spl radic D log 1 D). Video cameras are invariably bandwidth limited and this results in a trade-off between spatial and temporal resolution. Advances in sensor manufacturing technology have tremendously increased the available spatial resolution of modern cameras while simultaneously lowering the costs of these sensors. In stark contrast, hardware improvements in temporal resolution have been modest. One solution to enhance temporal resolution is to use high bandwidth imaging devices such as high speed sensors and camera arrays. Unfortunately, these solutions are expensive. An alternate solution is motivated by recent advances in computational imaging and compressive sensing. Camera designs based on these principles, typically, modulate the incoming video using spatio-temporal light modulators and capture the modulated video at a lower bandwidth. Reconstruction algorithms, motivated by compressive sensing, are subsequently used to recover the high bandwidth video at high fidelity. Though promising, these methods have been limited since they require complex and expensive light modulators that make the techniques difficult to realize in practice. In this paper, we show that a simple coded exposure modulation is sufficient to reconstruct high speed videos. We propose the Flutter Shutter Video Camera (FSVC) in which each exposure of the sensor is temporally coded using an independent pseudo-random sequence. Such exposure coding is easily achieved in modern sensors and is already a feature of several machine vision cameras. We also develop two algorithms for reconstructing the high speed video; the first based on minimizing the total variation of the spatio-temporal slices of the video and the second based on a data driven dictionary based approximation. We perform evaluation on simulated videos and real data to illustrate the robustness of our system. The theory of compressed sensing suggests that successful inversion of an image of the physical world (broadly defined to include speech signals, radar sonar returns, vibration records, sensor array snapshot vectors, 2-D images, and so on) for its source modes and amplitudes can be achieved at measurement dimensions far lower than what might be expected from the classical theories of spectrum or modal analysis, provided that the image is sparse in an apriori known basis. For imaging problems in spectrum analysis, and passive and active radar sonar, this basis is usually taken to be a DFT basis. However, in reality no physical field is sparse in the DFT basis or in any apriori known basis. No matter how finely we grid the parameter space the sources may not lie in the center of the grid cells and consequently there is mismatch between the assumed and the actual bases for sparsity. In this paper, we study the sensitivity of compressed sensing to mismatch between the assumed and the actual sparsity bases. We start by analyzing the effect of basis mismatch on the best k-term approximation error, which is central to providing exact sparse recovery guarantees. We establish achievable bounds for the l1 error of the best k -term approximation and show that these bounds grow linearly with the image (or grid) dimension and the mismatch level between the assumed and actual bases for sparsity. We then derive bounds, with similar growth behavior, for the basis pursuit l1 recovery error, indicating that the sparse recovery may suffer large errors in the presence of basis mismatch. Although, we present our results in the context of basis pursuit, our analysis applies to any sparse recovery principle that relies on the accuracy of best k-term approximations for its performance guarantees. We particularly highlight the problematic nature of basis mismatch in Fourier imaging, where spillage from off-grid DFT components turns a sparse representation into an incompressible one. We substantiate our mathematical analysis by numerical examples that demonstrate a considerable performance degradation for image inversion from compressed sensing measurements in the presence of basis mismatch, for problem sizes common to radar and sonar. Detecting and classifying targets in video streams from surveillance cameras is a cumbersome, error-prone and expensive task. Often, the incurred costs are prohibitive for real-time monitoring. This leads to data being stored locally or transmitted to a central storage site for post-incident examination. The required communication links and archiving of the video data are still expensive and this setup excludes preemptive actions to respond to imminent threats. An effective way to overcome these limitations is to build a smart camera that analyzes the data on-site, close to the sensor, and transmits alerts when relevant video sequences are detected. Deep neural networks (DNNs) have come to outperform humans in visual classifications tasks and are also performing exceptionally well on other computer vision tasks. The concept of DNNs and Convolutional Networks (ConvNets) can easily be extended to make use of higher-dimensional input data such as multispectral data. We explore this opportunity in terms of achievable accuracy and required computational effort. To analyze the precision of DNNs for scene labeling in an urban surveillance scenario we have created a dataset with 8 classes obtained in a field experiment. We combine an RGB camera with a 25-channel VIS-NIR snapshot sensor to assess the potential of multispectral image data for target classification. We evaluate several new DNNs, showing that the spectral information fused together with the RGB frames can be used to improve the accuracy of the system or to achieve similar accuracy with a 3x smaller computation effort. We achieve a very high per-pixel accuracy of 99.1 . Even for scarcely occurring, but particularly interesting classes, such as cars, 75 of the pixels are labeled correctly with errors occurring only around the border of the objects. This high accuracy was obtained with a training set of only 30 labeled images, paving the way for fast adaptation to various application scenarios. Iterative image reconstruction with sparsity-exploiting methods, such as total variation (TV) minimization, investigated in compressive sensing claim potentially large reductions in sampling requirements. Quantifying this claim for computed tomography (CT) is nontrivial, because both full sampling in the discrete-to-discrete imaging model and the reduction in sampling admitted by sparsity-exploiting methods are ill-defined. The present article proposes definitions of full sampling by introducing four sufficient-sampling conditions (SSCs). The SSCs are based on the condition number of the system matrix of a linear imaging model and address invertibility and stability. In the example application of breast CT, the SSCs are used as reference points of full sampling for quantifying the undersampling admitted by reconstruction through TV-minimization. In numerical simulations, factors affecting admissible undersampling are studied. Differences between few-view and few-detector bin reconstruction as well as a relation between object sparsity and admitted undersampling are quantified. Camera sensors can only capture a limited range of luminance simultaneously, and in order to create high dynamic range (HDR) images a set of different exposures are typically combined. In this paper we address the problem of predicting information that have been lost in saturated image areas, in order to enable HDR reconstruction from a single exposure. We show that this problem is well-suited for deep learning algorithms, and propose a deep convolutional neural network (CNN) that is specifically designed taking into account the challenges in predicting HDR values. To train the CNN we gather a large dataset of HDR images, which we augment by simulating sensor saturation for a range of cameras. To further boost robustness, we pre-train the CNN on a simulated HDR dataset created from a subset of the MIT Places database. We demonstrate that our approach can reconstruct high-resolution visually convincing HDR results in a wide range of situations, and that it generalizes well to reconstruction of images captured with arbitrary and low-end cameras that use unknown camera response functions and post-processing. Furthermore, we compare to existing methods for HDR expansion, and show high quality results also for image based lighting. Finally, we evaluate the results in a subjective experiment performed on an HDR display. This shows that the reconstructed HDR images are visually convincing, with large improvements as compared to existing methods. A 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 one-bit single-photon avalanche diode (SPAD) cameras. Natural signals and images are well known to be approximately sparse in transform domains such as wavelets and discrete cosine transform. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing exploits the sparsity of images or image patches in a transform domain or synthesis dictionary to reconstruct images from undersampled measurements. In this work, we focus on blind compressed sensing, where the underlying sparsifying transform is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the sparsifying transform from highly undersampled measurements. The proposed block coordinate descent-type algorithms involve highly efficient optimal updates. Importantly, we prove that although the proposed blind compressed sensing formulations are highly nonconvex, our algorithms are globally convergent (i.e., they converge from any initialization) to the set of critical points of the objectives def... For crowded scenes, the accuracy of object-based computer vision methods declines when the images are low-resolution and objects have severe occlusions. Taking counting methods for example, almost all the recent state-of-the-art counting methods bypass explicit detection and adopt regression-based methods to directly count the objects of interest. Among regression-based methods, density map estimation, where the number of objects inside a subregion is the integral of the density map over that subregion, is especially promising because it preserves spatial information, which makes it useful for both counting and localization (detection and tracking). With the power of deep convolutional neural networks (CNNs) the counting performance has improved steadily. The goal of this paper is to evaluate density maps generated by density estimation methods on a variety of crowd analysis tasks, including counting, detection, and tracking. Most existing CNN methods produce density maps with resolution that is smaller than the original images, due to the downsample strides in the convolution pooling operations. To produce an original-resolution density map, we also evaluate a classical CNN that uses a sliding window regressor to predict the density for every pixel in the image. We also consider a fully convolutional (FCNN) adaptation, with skip connections from lower convolutional layers to compensate for loss in spatial information during upsampling. In our experiments, we found that the lower-resolution density maps sometimes have better counting performance. In contrast, the original-resolution density maps improved localization tasks, such as detection and tracking, compared to bilinear upsampling the lower-resolution density maps. Finally, we also propose several metrics for measuring the quality of a density map, and relate them to experiment results on counting and localization. Most multispectral remote sensors (e.g. QuickBird, IKONOS, and Landsat 7 ETM+) provide low-spatial high-spectral resolution multispectral (MS) or high-spatial low-spectral resolution panchromatic (PAN) images, separately. In order to reconstruct a high-spatial high-spectral resolution multispectral image volume, either the information in MS and PAN images are fused (i.e. pansharpening) or super-resolution reconstruction (SRR) is used with only MS images captured on different dates. Existing methods do not utilize temporal information of MS and high spatial resolution of PAN images together to improve the resolution. In this paper, we propose a multiframe SRR algorithm using pansharpened MS images, taking advantage of both temporal and spatial information available in multispectral imagery, in order to exceed spatial resolution of given PAN images. We first apply pansharpening to a set of multispectral images and their corresponding PAN images captured on different dates. Then, we use the pansharpened multispectral images as input to the proposed wavelet-based multiframe SRR method to yield full volumetric SRR. The proposed SRR method is obtained by deriving the subband relations between multitemporal MS volumes. We demonstrate the results on Landsat 7 ETM+ images comparing our method to conventional techniques.