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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.
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
Distributed Sensor Perception via Sparse Representation
 THE PROCEEDINGS OF IEEE
"... Sensor network scenarios are considered where the underlying signals of interest exhibit a degree of sparsity, which means that in an appropriate basis, they can be expressed in terms of a small number of nonzero coefficients. Following the emerging theory of compressive sensing, an overall architec ..."
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Cited by 16 (2 self)
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Sensor network scenarios are considered where the underlying signals of interest exhibit a degree of sparsity, which means that in an appropriate basis, they can be expressed in terms of a small number of nonzero coefficients. Following the emerging theory of compressive sensing, an overall architecture is considered where the sensors acquire potentially noisy projections of the data, and the underlying sparsity is exploited to recover useful information about the signals of interest, which will be referred to as distributed sensor perception. First, we discuss the question of which projections of the data should be acquired, and how many of them. Then, we discuss how to take advantage of possible joint sparsity of the signals acquired by multiple sensors, and show how this can further improve the inference of the events from the sensor network. Two practical sensor applications are demonstrated, namely, distributed wearable action recognition using lowpower motion sensors and distributed object recognition using highpower camera sensors. Experimental data support the utility of the compressive sensing framework in distributed sensor perception.
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.
1 A Multiscale Algorithm for Reconstructing Videos from Streaming Compressive Measurements
"... We propose a multiscale, iterative algorithm for reconstructing video signals from streaming compressive measurements. Our algorithm is based on the observation that, at the imaging sensor, many videos should have limited temporal bandwidth due to the spatial lowpass filtering that is inherent in ty ..."
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Cited by 11 (1 self)
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We propose a multiscale, iterative algorithm for reconstructing video signals from streaming compressive measurements. Our algorithm is based on the observation that, at the imaging sensor, many videos should have limited temporal bandwidth due to the spatial lowpass filtering that is inherent in typical imaging systems. Under modest assumptions about the motion of objects in the scene, this spatial filtering prevents the temporal complexity of the video from being arbitrarily high. Thus, even though streaming measurement systems may measure a video thousands of times per second, we propose an algorithm that only involves reconstructing a much lower rate stream of “anchor frames. ” Our analysis of the temporal complexity of videos reveals an interesting tradeoff between the spatial resolution of the camera, the speed of any moving objects, and the temporal bandwidth of the video. We leverage this tradeoff in proposing a multiscale reconstruction algorithm that alternates between video reconstruction and motion estimation as it produces finer resolution estimates of the video.
A Tutorial on Encoding and Wireless Transmission of Compressively Sampled Videos
 IEEE Comm. Surveys and Tutorials
"... Abstract—Compressed sensing (CS) has emerged as a promising technique to jointly sense and compress sparse signals. One of the most promising applications of CS is compressive imaging. Leveraging the fact that images can be represented as approximately sparse signals in a transformed domain, images ..."
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Cited by 6 (4 self)
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Abstract—Compressed sensing (CS) has emerged as a promising technique to jointly sense and compress sparse signals. One of the most promising applications of CS is compressive imaging. Leveraging the fact that images can be represented as approximately sparse signals in a transformed domain, images can be compressed and sampled simultaneously using lowcomplexity linear operations. Recently, these techniques have been extended beyond imaging to encode video. Much of the compression in traditional video encoding comes from using motion vectors to take advantage of the temporal correlation between adjacent frames. However, calculating motion vectors is a processingintensive operation that causes significant power consumption. Therefore, any technique appropriate for resource constrained video sensors must exploit temporal correlation through lowcomplexity operations. In this tutorial, we first briefly discuss challenges involved in the transmission of video over a wireless multimedia sensor network (WMSN). We then discuss the different techniques available for applying CS encoding first to images, and then to videos for errorresilient transmission in lossy channels. Existing solutions are examined, and compared in terms of applicability to wireless multimedia sensor networks (WMSNs). Finally, open issues are discussed and future research trends are outlined. Index Terms—Compressed Sensing, Multimedia communication, Wireless sensor networks, Video coding, Energyratedistortion.
DICTIONARY LEARNINGBASED DISTRIBUTED COMPRESSIVE VIDEO SENSING +
"... We address an important issue of fully lowcost and lowcomplex video compression for use in resourceextremely limited sensors/devices. Conventional motion estimationbased video compression or distributed video coding (DVC) techniques all rely on the highcost mechanism, namely, sensing/sampling a ..."
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Cited by 6 (1 self)
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We address an important issue of fully lowcost and lowcomplex video compression for use in resourceextremely limited sensors/devices. Conventional motion estimationbased video compression or distributed video coding (DVC) techniques all rely on the highcost mechanism, namely, sensing/sampling and compression are disjointedly performed, resulting in unnecessary consumption of resources. That is, most acquired raw video data will be discarded in the (possibly) complex compression stage. In this paper, we propose a dictionary learningbased distributed compressive video sensing (DCVS) framework to “directly” acquire compressed video data. Embedded in the compressive sensing (CS)based singlepixel camera architecture, DCVS can compressively sense each video frame in a distributed manner. At DCVS decoder, video reconstruction can be formulated as an l 1
Distributed Representation of Geometrically Correlated Images with Compressed Linear Measurements
, 2010
"... Abstract—This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or the camera positioning. It concentrates on the problem where images are encoded with compressed linear measurements. We propose a geometrybased correlation model that de ..."
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Cited by 5 (4 self)
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Abstract—This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or the camera positioning. It concentrates on the problem where images are encoded with compressed linear measurements. We propose a geometrybased correlation model that describes the common information in pairs of images. We assume that the constitutive components of natural images can be captured by visual features that undergo local transformations (e.g., translation) in different images. We first identify prominent visual features by computing a sparse approximation of a reference image with a dictionary of geometric basis functions. We then pose a regularized optimization problem in order to estimate the corresponding features in correlated images that are given by quantized linear measurements. The correlation model is thus given by the relative geometric transformations between corresponding features. We then propose an efficient joint decoding algorithm that reconstructs the compressed images such that they are consistent with both the quantized measurements and the correlation model. Experimental results show that the proposed algorithm effectively estimates the correlation between images in multiview data sets. In addition, the proposed algorithm provides effective decoding performance that advantageously compares to independent coding solutions and stateoftheart distributed coding schemes based on disparity learning. Index Terms—Correlation estimation, geometric transformations, quantization, random projections, sparse approximations. I.
Compressive Video Streaming: Design and RateEnergyDistortion Analysis
 IEEE Trans. on Multimedia, In Press
, 2013
"... Abstract—Realtime encoding and errorresilient wireless transmission of multimedia content using traditional encoding techniques requires relatively high processing and transmission power, while pervasive surveillance and monitoring systems often referred to as wireless multimedia sensor networks ( ..."
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Cited by 4 (3 self)
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Abstract—Realtime encoding and errorresilient wireless transmission of multimedia content using traditional encoding techniques requires relatively high processing and transmission power, while pervasive surveillance and monitoring systems often referred to as wireless multimedia sensor networks (WMSNs) [1] are generally composed of lowpower, lowcomplexity devices. To bridge this gap, this article introduces and analyzes a compressive video sensing (CVS) encoder designed to reduce the required energy and computational complexity at the source node. The proposed encoder leverages the properties of compressed sensing (CS) to overcome many of the limitations of traditional encoding techniques, specifically lack of resilience to channel errors, and high computational complexity. Recognizing the inadequacy of traditional ratedistortion analysis to account for the constraints introduced by resourcelimited devices, we introduce the notion of rateenergydistortion, based on which we develop an analytical/empirical model that predicts the received video quality when the overall energy available for both encoding and transmission of each frame of a video is fixed and limited and the transmissions are affected by channel errors. The model allows comparing the received video quality, computation time, and energy consumption per frame of different wireless streaming systems, and can be used to determine the optimal allocation of encoded video rate and channel encoding rate for a given available energy budget. Based on the proposed model, we show that the CVS video encoder outperforms (in an energy constrained system) two common encoders suitable for a wireless multimedia sensor network environment; H.264/AVC intra and motion JPEG (MJPEG). Extensive results show that CVS is able to deliver video at good quality (an SSIM value of 0.8) through lossy wireless networks with lower energy consumption per frame than competing encoders. Index Terms—Compressed sensing, video surveillance, video encoding, multimedia sensor networks. I.