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42
A multiscale framework for compressive sensing of video
 in Proc. Picture Coding Symposium (PCS
, 2009
"... Compressive Sensing (CS) allows the highly efficient acquisition of many signals that could be difficult to capture or encode using conventional methods. From a relatively small number of random measurements, a highdimensional signal can be recovered if it has a sparse or nearsparse representation ..."
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Cited by 56 (9 self)
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Compressive Sensing (CS) allows the highly efficient acquisition of many signals that could be difficult to capture or encode using conventional methods. From a relatively small number of random measurements, a highdimensional signal can be recovered if it has a sparse or nearsparse representation in a basis known to the decoder. In this paper, we consider the application of CS to video signals in order to lessen the sensing and compression burdens in single and multicamera imaging systems. In standard video compression, motion compensation and estimation techniques have led to improved sparse representations that are more easily compressible; we adapt these techniques for the problem of CS recovery. Using a coarsetofine reconstruction algorithm, we alternate between the tasks of motion estimation and motioncompensated waveletdomain signal recovery. We demonstrate that our algorithm allows the recovery of video sequences from fewer measurements than either framebyframe or interframe difference recovery methods. 1.
LowDimensional Models for Dimensionality Reduction and Signal Recovery: A Geometric Perspective
, 2009
"... We compare and contrast from a geometric perspective a number of lowdimensional signal models that support stable informationpreserving dimensionality reduction. We consider sparse and compressible signal models for deterministic and random signals, structured sparse and compressible signal model ..."
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Cited by 47 (12 self)
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We compare and contrast from a geometric perspective a number of lowdimensional signal models that support stable informationpreserving dimensionality reduction. We consider sparse and compressible signal models for deterministic and random signals, structured sparse and compressible signal models, point clouds, and manifold signal models. Each model has a particular geometrical structure that enables signal information in to be stably preserved via a simple linear and nonadaptive projection to a much lower dimensional space whose dimension either is independent of the ambient dimension at best or grows logarithmically with it at worst. As a bonus, we point out a common misconception related to probabilistic compressible signal models, that is, that the generalized Gaussian and Laplacian random models do not support stable linear dimensionality reduction.
Compressed sensing in astronomy
"... Recent advances in signal processing have focused on the use of sparse representations in various applications. A new field of interest based on sparsity has recently emerged: compressed sensing. This theory is a new sampling framework that provides an alternative to the wellknown Shannon sampling ..."
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Cited by 39 (1 self)
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Recent advances in signal processing have focused on the use of sparse representations in various applications. A new field of interest based on sparsity has recently emerged: compressed sensing. This theory is a new sampling framework that provides an alternative to the wellknown Shannon sampling theory. In this paper we investigate how compressed sensing (CS) can provide new insights into astronomical data compression and more generally how it paves the way for new conceptions in astronomical remote sensing. We first give a brief overview of the compressed sensing theory which provides very simple coding process with low computational cost, thus favoring its use for realtime applications often found on board space mission. We introduce a practical and effective recovery algorithm for decoding compressed data. In astronomy, physical prior information is often crucial for devising effective signal processing methods. We particularly point out that a CSbased compression scheme is flexible enough to account for such information. In this context, compressed sensing is a new framework in which data acquisition and data processing are merged. We show also that CS provides a new fantastic way to handle multiple observations of the same field view, allowing us to recover information at very low signaltonoise ratio, which is impossible with standard compression methods. This CS data fusion concept could lead to an elegant and effective way to solve the problem ESA is faced with, for the transmission to the earth of the data collected by PACS, one of the instruments on board the Herschel spacecraft which will launched in 2008.
P2c2: Programmable pixel compressive camera for high speed imaging
 Computer Vision and Pattern Recognition, IEEE Computer Society Conference on
, 2011
"... 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 cam ..."
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Cited by 38 (6 self)
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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 framerate. 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 superresolution. 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 spatiotemporal redundancies in a video volume, one can faithfully recover the underlying highspeed video frames from the observed low speed coded video. The imaging architecture and the reconstruction algorithm allows us to achieve temporal superresolution 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. 1.
Kronecker Compressive Sensing
"... Compressive sensing (CS) is an emerging approach for acquisition of signals having a sparse or compressible representation in some basis. While the CS literature has mostly focused on problems involving 1D signals and 2D images, many important applications involve signals that are multidimensional ..."
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Cited by 38 (2 self)
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Compressive sensing (CS) is an emerging approach for acquisition of signals having a sparse or compressible representation in some basis. While the CS literature has mostly focused on problems involving 1D signals and 2D images, many important applications involve signals that are multidimensional; in this case, CS works best with representations that encapsulate the structure of such signals in every dimension. We propose the use of Kronecker product matrices in CS for two purposes. First, we can use such matrices as sparsifying bases that jointly model the different types of structure present in the signal. Second, the measurement matrices used in distributed settings can be easily expressed as Kronecker product matrices. The Kronecker product formulation in these two settings enables the derivation of analytical bounds for sparse approximation of multidimensional signals and CS recovery performance as well as a means to evaluate novel distributed measurement schemes. I.
1 Compressive Video Sampling with Approximate Message Passing Decoding
"... In this paper, we apply compressed sensing to video compression. Compressed sensing (CS) techniques exploit the observation that one needs much fewer random measurements than given by the ShannonNyquist sampling theory to recover an object if this object is compressible (i.e., sparse in the spatial ..."
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Cited by 38 (2 self)
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In this paper, we apply compressed sensing to video compression. Compressed sensing (CS) techniques exploit the observation that one needs much fewer random measurements than given by the ShannonNyquist sampling theory to recover an object if this object is compressible (i.e., sparse in the spatial domain or in a transform domain). In the CS framework, we can achieve sensing, compression and denoising simultaneously. We propose a fast and simple online encoding by application of pseudorandom downsampling of the twodimensional fast Fourier transform to video frames. For offline decoding, we apply a modification of the recently proposed approximate message passing (AMP) algorithm. The AMP method has been derived using the statistical concept of ’state evolution’, and it has been shown to considerably accelerate the convergence rate in special CSdecoding applications. We shall prove that the AMP method can be rewritten as a forwardbackward splitting algorithm. This new representation enables us to give conditions that ensure convergence of the AMP method and to modify the algorithm in order to achieve higher robustness. The success of reconstruction methods for video decoding also essentially depends on the chosen transform, where sparsity of the video signals is assumed. We propose to incorporate the 3D dualtree complex wavelet transform that possesses sufficiently good properties of directional selectivity and shift invariance while being computationally less expensive and less redundant than other directional 3D wavelet transforms.
Video from a single coded exposure photograph using a learned overcomplete dictionary, inIEEEIntl.Conf.Comp. Vision
, 2011
"... Cameras face a fundamental tradeoff between the spatial and temporal resolution – digital still cameras can capture images with high spatial resolution, but most highspeed video cameras suffer from low spatial resolution. It is hard to overcome this tradeoff without incurring a significant increase ..."
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Cited by 34 (2 self)
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Cameras face a fundamental tradeoff between the spatial and temporal resolution – digital still cameras can capture images with high spatial resolution, but most highspeed video cameras suffer from low spatial resolution. It is hard to overcome this tradeoff without incurring a significant increase in hardware costs. In this paper, we propose techniques for sampling, representing and reconstructing the spacetime volume in order to overcome this tradeoff. Our approach has two important distinctions compared to previous works: (1) we achieve sparse representation of videos by learning an overcomplete dictionary on video patches, and (2) we adhere to practical constraints on sampling scheme which is imposed by architectures of present image sensor devices. Consequently, our sampling scheme can be implemented on image sensors by making a straightforward modification to the control unit. To demonstrate the power of our approach, we have implemented a prototype imaging system with perpixel coded exposure control using a liquid crystal on silicon (LCoS) device. Using both simulations and experiments on a wide range of scenes, we show that our method can effectively reconstruct a video from a single image maintaining high spatial resolution. 1.
Compressive coded aperture imaging
 Proc. SPIE
, 2009
"... Nonlinear image reconstruction based upon sparse representations of images has recently received widespread attention with the emerging framework of compressed sensing (CS). This theory indicates that, when feasible, judicious selection of the type of distortion induced by measurement systems may dr ..."
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Cited by 24 (1 self)
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Nonlinear image reconstruction based upon sparse representations of images has recently received widespread attention with the emerging framework of compressed sensing (CS). This theory indicates that, when feasible, judicious selection of the type of distortion induced by measurement systems may dramatically improve our ability to perform image reconstruction. However, applying compressed sensing theory to practical imaging systems poses a key challenge: physical constraints typically make it infeasible to actually measure many of the random projections described in the literature, and therefore, innovative and sophisticated imaging systems must be carefully designed to effectively exploit CS theory. In video settings, the performance of an imaging system is characterized by both pixel resolution and field of view. In this work, we propose compressive imaging techniques for improving the performance of video imaging systems in the presence of constraints on the focal plane array size. In particular, we describe a novel yet practical approach that combines coded aperture imaging to enhance pixel resolution with superimposing subframes of a scene onto a single focal plane array to increase field of view. Specifically, the proposed method superimposes coded observations and uses waveletbased sparsity recovery algorithms to reconstruct the original subframes. We demonstrate the effectiveness of this approach by reconstructing with high resolution the constituent images of a video sequence.
Prasanna “Compressedsensingenabled Video Streaming for Wireless Multimedia Sensor Networks
 IEEE Transactions on Mobile Computing
"... Abstract—This paper presents the design of a networked system for joint compression, rate control and error correction of video over resourceconstrained embedded devices based on the theory of Compressed Sensing (CS). The objective of this work is to design a crosslayer system that jointly control ..."
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Cited by 23 (7 self)
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Abstract—This paper presents the design of a networked system for joint compression, rate control and error correction of video over resourceconstrained embedded devices based on the theory of Compressed Sensing (CS). The objective of this work is to design a crosslayer system that jointly controls the video encoding rate, the transmission rate, and the channel coding rate to maximize the received video quality. First, compressed sensingbased video encoding for transmission over Wireless Multimedia Sensor Networks (WMSNs) is studied. It is shown that compressed sensing can overcome many of the current problems of video over WMSNs, primarily encoder complexity and low resiliency to channel errors. A rate controller is then developed with the objective of maintaining fairness among different videos while maximizing the received video quality. It is shown that the rate of Compressed Sensed Video (CSV) can be predictably controlled by varying only the compressed sensing sampling rate. It is then shown that the developed rate controller can be interpreted as the iterative solution to a convex optimization problem representing the optimization of the rate allocation across the network. The error resiliency properties of compressed sensed images and videos are then studied, and an optimal error detection and correction scheme is presented for video transmission over lossy channels. Finally, the entire system is evaluated through simulation and test bed evaluation. The rate controller is shown to outperform existing TCPfriendly rate control schemes in terms of both fairness and received video quality. The test bed results show that the rates converge to stable values in real channels. Index Terms—Compressed sensing, optimization, multimedia content, congestion control, sensor networks. Ç
ModelBased Compressive Sensing for Signal Ensembles
"... Abstract—Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for acquiring sparse or compressible signals. Instead of taking N periodic samples, we measure M ≪ N inner products with random vectors and then recover the signal via a sparsityseeking optimization or greedy algorithm. ..."
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Cited by 14 (3 self)
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Abstract—Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for acquiring sparse or compressible signals. Instead of taking N periodic samples, we measure M ≪ N inner products with random vectors and then recover the signal via a sparsityseeking optimization or greedy algorithm. A new framework for CS based on unions of subspaces can improve signal recovery by including dependencies between values and locations of the signal’s significant coefficients. In this paper, we extend this framework to the acquisition of signal ensembles under a common sparse supports model. The new framework provides recovery algorithms with theoretical performance guarantees. Additionally, the framework scales naturally to large sensor networks: the number of measurements needed for each signal does not increase as the network becomes larger. Furthermore, the complexity of the recovery algorithm is only linear in the size of the network. We provide experimental results using synthetic and realworld signals that confirm these benefits. I.