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15
Adaptive Compressed Image Sensing Using Dictionaries
"... Abstract. In recent years, the theory of Compressed Sensing has emerged as an alternative for the Shannon sampling theorem, suggesting that compressible signals can be reconstructed from far fewer samples than required by the Shannon sampling theorem. In fact the theory advocates that nonadaptive, ..."
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Abstract. In recent years, the theory of Compressed Sensing has emerged as an alternative for the Shannon sampling theorem, suggesting that compressible signals can be reconstructed from far fewer samples than required by the Shannon sampling theorem. In fact the theory advocates that nonadaptive, ‘random ’ functionals are in some sense optimal for this task. However, in practice Compressed Sensing is very difficult to implement for large data sets, since the algorithms are exceptionally slow and have high memory consumption. In this work, we present a new alternative method for simultaneous image acquisition and compression called Adaptive Compressed Sampling. Our approach departs fundamentally from the (non adaptive) Compressed Sensing mathematical framework by replacing the ‘universal ’ acquisition of incoherent measurements with a direct and fast method for adaptive transform coefficient acquisition. The main advantages of this direct approach are that no complex recovery algorithm is in fact needed and that it allows more control over the compressed image quality, in particular, the sharpness of edges. Our experimental results show that our adaptive algorithms perform better than existing nonadaptive methods in terms of image quality and speed.
Infogreedy sequential adaptive compressed sensing,” arXiv preprint arXiv:1407.0731
, 2014
"... Abstract—We present an informationtheoretic framework for sequential adaptive compressed sensing, InfoGreedy Sensing, where measurements are chosen to maximize the extracted information conditioned on the previous measurements. We show that the widely used bisection approach is InfoGreedy for a ..."
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Abstract—We present an informationtheoretic framework for sequential adaptive compressed sensing, InfoGreedy Sensing, where measurements are chosen to maximize the extracted information conditioned on the previous measurements. We show that the widely used bisection approach is InfoGreedy for a family ofsparse signals by connecting compressed sensing and blackbox complexity of sequential query algorithms, and present InfoGreedy algorithms for Gaussian andGaussian mixture model (GMM) signals, as well as ways to design sparse InfoGreedy measurements. Numerical examples demonstrate the good performance of the proposed algorithms using simulated and real data: InfoGreedy Sensing shows significant improvement over random projection for signals with sparse and lowrank covariance matrices, and adaptivity brings robustness when there is a mismatch between the assumed and the true distributions. Index Terms—Compressed sensing, adaptive estimation, adaptive signal detection, mutual information. I.
Compression Schemes for TimeVarying Sparse Signals
"... Abstract—In this paper, we will investigate an adaptive compression scheme for tracking timevarying sparse signals with possibly varying sparsity patterns and/or order. In particular, we will focus on sparse sensing, which enables a completely distributed compression and simplifies the sampling ar ..."
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Abstract—In this paper, we will investigate an adaptive compression scheme for tracking timevarying sparse signals with possibly varying sparsity patterns and/or order. In particular, we will focus on sparse sensing, which enables a completely distributed compression and simplifies the sampling architecture. The sensing matrix is designed at each time step based on the entire history of measurements and known dynamics such that the information gain is maximized. We illustrate the developed theory with a target tracking example. Finally, we provide a few extensions of the proposed framework to include a richer class of sparse signals, e.g., structured sparsity and smoothness. Index Terms—Structured sensing, sensor selection, sparsityaware Kalman filter, sparse sensing, adaptive compressed sensing, distributed compression, big data. I.
OPPORTUNISTIC SENSING FOR OBJECT RECOGNITION — A UNIFIED FORMULATION FOR DYNAMIC SENSOR SELECTION AND FEATURE EXTRACTION
"... A novel problem of object recognition with dynamically allocated sensing resources is considered in this paper. We call this problem opportunistic sensing since prior knowledge about the correlation between class label and signal distribution is exploited as early as in data acquisition. Two form ..."
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A novel problem of object recognition with dynamically allocated sensing resources is considered in this paper. We call this problem opportunistic sensing since prior knowledge about the correlation between class label and signal distribution is exploited as early as in data acquisition. Two forms of sensing parameters – discrete sensor index and continuous linear measurement vector – are optimized within the same maximum negative entropy framework. The computationally intractable expected entropy is approximated using unscented transform for Gaussian models, and we solve the problem using a gradientbased method. Our formulation is theoretically shown to be closely related to the maximum mutual information criterion for sensor selection and linear feature extraction techniques such as PCA, LDA, and CCA. The proposed approach is validated on multiview vehicle classification and face recognition datasets, and remarkable improvement over baseline methods is demonstrated in the experiments. Index Terms — opportunistic sensing, view selection, feature extraction, objection recognition 1.
Subspace Communication
, 2014
"... We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by ..."
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We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by a fixed assignment of spectrum resources by regulatory agencies. This has resulted into a blind alley, as current wireless spectrum has become an expensive and a scarce resource. However, recent measurements in dense areas paint a very different picture: there is an actual underutilization of the spectrum by legacy systems. Cognitive radio exhibits a tremendous promise for increasing the spectral efficiency for future wireless systems. Ideally, new secondary users would have a perfect panorama of the spectrum usage, and would opportunistically communicate over the available resources without degrading the primary systems. Yet in practice, monitoring the spectrum resources, detecting available resources for opportunistic communication, and transmitting over the resources are hard tasks. This thesis addresses the tasks of monitoring, de
Nonuniform Sampling Walls in Wideband Signal Detection
"... Abstract—This work shows the existence of sampling walls in detection of wideband signals from Bernoulli nonuniform sampling (BNS) in the presence of noise uncertainty. A sampling wall is defined as the sampling density below which the target error probabilities, i.e., the missed detection and false ..."
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Abstract—This work shows the existence of sampling walls in detection of wideband signals from Bernoulli nonuniform sampling (BNS) in the presence of noise uncertainty. A sampling wall is defined as the sampling density below which the target error probabilities, i.e., the missed detection and false alarm probabilities, cannot be guaranteed at a given signal to noise ratio (SNR) regardless the number of acquired samples. The BNS is adopted because it exhibits good tradeoff properties between complexity and performance. It is shown that BNS suffers from noise enhancement, which translates into a whitening effect in the correlation of the legacy signal. Contrarily to the existing literature, the signal detection problem is addressed without having to reconstruct neither the signal nor its spectrum. More specifically, the optimal low SNR detector is formulated as a generalized likelihood ratio test (GLRT) to exploit the available side information of the problem, i.e., the noise variance, the sampling density and the legacy signal autocorrelation. By deriving the asymptotic performance of the GLRT in the presence of noise uncertainty, explicit expressions for sampling walls are obtained as a function of the legacy signal occupancy, the SNR and the noise uncertainty. Further, numerical results are provided to assess the behavior of the sampling walls and signal detection performance. Index Terms—Bernoulli nonuniform sampling, GLRT, sampling walls, SNR walls, cognitive radio.
1 Sequential Bayesian Sparse Signal Reconstruction using Array Data
"... Abstract—In this paper, the sequential reconstruction of source waveforms under a sparsity constraint is considered from a Bayesian perspective. Let the wave field which is observed by a sensor array be caused by a spatiallysparse set of sources. A spatially weighted Laplacelike prior is assumed f ..."
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Abstract—In this paper, the sequential reconstruction of source waveforms under a sparsity constraint is considered from a Bayesian perspective. Let the wave field which is observed by a sensor array be caused by a spatiallysparse set of sources. A spatially weighted Laplacelike prior is assumed for the source field and the corresponding weighted Least Absolute Shrinkage and Selection Operator (LASSO) cost function is derived. After the weighted LASSO solution has been calculated as the maximum a posteriori estimate at time step k, the posterior distribution of the source amplitudes is analytically approximated. The weighting of the Laplacelike prior for time step k + 1 is then fitted to the approximated posterior distribution. This results in a sequential update for the LASSO weights. Thus, a sequence of weighted LASSO problems is solved for estimating the temporal evolution of a sparse source field. The method is evaluated numerically using a uniform linear array in simulations and applied to data which were acquired from a towed horizontal array during the long range acoustic communications experiment. Index Terms—sequential estimation, Bayesian estimation, sparsity, weighted LASSO.
OPPORTUNISTIC SENSING FOR OBJECT RECOGNITION — A UNIFIED FORMULATION FOR DYNAMIC SENSOR SELECTION AND FEATURE EXTRACTION
"... A novel problem of object recognition with dynamically allocated sensing resources is considered in this paper. We call this problem opportunistic sensing since prior knowledge about the correlation between class label and signal distribution is exploited as early as in data acquisition. Two forms o ..."
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A novel problem of object recognition with dynamically allocated sensing resources is considered in this paper. We call this problem opportunistic sensing since prior knowledge about the correlation between class label and signal distribution is exploited as early as in data acquisition. Two forms of sensing parameters – discrete sensor index and continuous linear measurement vector – are optimized within the same maximum negative entropy framework. The computationally intractable expected entropy is approximated using unscented transform for Gaussian models, and we solve the problem using a gradientbased method. Our formulation is theoretically shown to be closely related to the maximum mutual information criterion for sensor selection and linear feature extraction techniques such as PCA, LDA, and CCA. The proposed approach is validated on multiview vehicle classification and face recognition datasets, and remarkable improvement over baseline methods is demonstrated in the experiments. Index Terms — opportunistic sensing, view selection, feature extraction, objection recognition 1.
6344 IEEE TRANSACTIONS ON SIGNAL PROCESSING Sequential Bayesian Sparse Signal Reconstruction Using Array Data
"... Abstract—In this paper, the sequential reconstruction of source waveforms under a sparsity constraint is considered from a Bayesian perspective. Let the wave field, which is observed by a sensor array, be caused by a spatiallysparse set of sources. A spatially weighted Laplacelike prior is assumed ..."
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Abstract—In this paper, the sequential reconstruction of source waveforms under a sparsity constraint is considered from a Bayesian perspective. Let the wave field, which is observed by a sensor array, be caused by a spatiallysparse set of sources. A spatially weighted Laplacelike prior is assumed for the source field and the corresponding weighted Least Absolute Shrinkage and Selection Operator (LASSO) cost function is derived. After the weighted LASSO solution has been calculated as the maximum a posteriori estimate at time step, the posterior distribution of the source amplitudes is analytically approximated. The weighting of the Laplacelike prior for time step is then fitted to the approximated posterior distribution. This results in a sequential update for the LASSO weights. Thus, a sequence of weighted LASSO problems is solved for estimating the temporal evolution of a sparse source field. The method is evaluated numerically using a uniform linear array in simulations and applied to data which were acquired from a towed horizontal array during the long range acoustic communications experiment. Index Terms—Bayesian estimation, sequential estimation, sparsity, weighted LASSO. I.
1AdaptiveRate Compressive Sensing Using Side Information
"... Abstract—We provide two novel adaptiverate compressive sensing (CS) strategies for sparse, timevarying signals using side information. Our first method utilizes extra crossvalidation measurements, and the second one exploits extra lowresolution measurements. Unlike the majority of current CS tec ..."
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Abstract—We provide two novel adaptiverate compressive sensing (CS) strategies for sparse, timevarying signals using side information. Our first method utilizes extra crossvalidation measurements, and the second one exploits extra lowresolution measurements. Unlike the majority of current CS techniques, we do not assume that we know an upper bound on the number of significant coefficients that comprise the images in the video sequence. Instead, we use the side information to predict the number of significant coefficients in the signal at the next time instant. For each image in the video sequence, our techniques specify a fixed number of spatiallymultiplexed CS measurements to acquire, and adjust this quantity from image to image. Our strategies are developed in the specific context of background subtraction for surveillance video, and we experimentally validate the proposed methods on real video sequences. Index Terms—Compressive sensing, cross validation, opportunistic sensing, background subtraction I.