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29
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.
Compressive Acquisition of Dynamic Scenes
"... Compressive sensing (CS) is a new approach for the acquisition and recovery of sparse signals and images that enables sampling rates significantly below the classical Nyquist rate. Despite significant progress in the theory and methods of CS, little headway has been made in compressive video acquis ..."
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Cited by 37 (10 self)
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Compressive sensing (CS) is a new approach for the acquisition and recovery of sparse signals and images that enables sampling rates significantly below the classical Nyquist rate. Despite significant progress in the theory and methods of CS, little headway has been made in compressive video acquisition and recovery. Video CS is complicated by the ephemeral nature of dynamic events, which makes direct extensions of standard CS imaging architectures and signal models infeasible. In this paper, we develop a new framework for video CS for dynamic textured scenes that models the evolution of the scene as a linear dynamical system (LDS). This reduces the video recovery problem to first estimating the model parameters of the LDS from compressive measurements, from which the image frames are then reconstructed. We exploit the lowdimensional dynamic parameters (the state sequence) and highdimensional static parameters (the observation matrix) of the LDS to devise a novel compressive measurement strategy that measures only the dynamic part of the scene at each instant and accumulates measurements over time to estimate the static parameters. This enables us to considerably lower the compressive measurement rate considerably. We validate our approach with a range of experiments including classification experiments that highlight the effectiveness of the proposed approach.
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.
Anomaly detection and reconstruction from random projections
 IEEE Transactions on Image Processing
"... Abstract—Compressedsensing methodology typically employs random projections simultaneously with signal acquisition to accomplish dimensionality reduction within a sensor device. The effect of such random projections on the preservation of anomalous data is investigated. The popular RX anomaly det ..."
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Cited by 9 (2 self)
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Abstract—Compressedsensing methodology typically employs random projections simultaneously with signal acquisition to accomplish dimensionality reduction within a sensor device. The effect of such random projections on the preservation of anomalous data is investigated. The popular RX anomaly detector is derived for the case in which global anomalies are to be identified directly in the randomprojection domain, and it is determined via both random simulation, as well as empirical observation that strongly anomalous vectors are likely to be identifiable by the projectiondomain RX detector even in lowdimensional projections. Finally, a reconstruction procedure for hyperspectral imagery is developed wherein projectiondomain anomaly detection is employed to partition the data set, permitting anomaly and normal pixel classes to be separately reconstructed in order to improve the representation of the anomaly pixels. Index Terms—Anomaly detection, compressed sensing (CS), hyperspectral data, principal component analysis (PCA). I.
Reprocs: A missing link between recursive robust pca and recursive sparse recovery in large but correlated noise
 CoRR
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Sketched SVD: Recovering spectral features from compressive measurements. ArXiv eprints
, 2012
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Classification and Reconstruction From Random Projections for Hyperspectral Imagery
"... Abstract—There is increasing interest in dimensionality reduction through random projections due in part to the emerging paradigm of compressed sensing. It is anticipated that signal acquisition with random projections will decrease signalsensing costs significantly; moreover, it has been demonstra ..."
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Cited by 4 (2 self)
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Abstract—There is increasing interest in dimensionality reduction through random projections due in part to the emerging paradigm of compressed sensing. It is anticipated that signal acquisition with random projections will decrease signalsensing costs significantly; moreover, it has been demonstrated that both supervised and unsupervised statistical learning algorithms work reliably within randomly projected subspaces. Capitalizing on this latter development, several classdependent strategies are proposed for the reconstruction of hyperspectral imagery from random projections. In this approach, each hyperspectral pixel is first classified into one of several pixel groups using either a conventional supervised classifier or an unsupervised clustering algorithm. After the grouping procedure, a suitable reconstruction method, such as compressive projection principal component analysis, is employed independently within each group. Experimental results confirm that such classdependent reconstruction, which employs statistics pertinent to each class as opposed to the global statistics estimated over the entire data set, results in more accurate reconstructions of hyperspectral pixels from random projections. Index Terms—Dimensionality reduction, Gaussian mixture model (GMM), hyperspectral data, random projection, support
Decoderside dimensionality determination for compressiveprojection principal component analysis of hyperspectral data
 in Proc. Int. Conf. Image Process
, 2011
"... Compressiveprojection principal component analysis reconstructs vectors from random projections by recovering an approximation to the principal eigenvectors of the principalcomponent transform. A heuristic for the number of eigenvectors to approximate is developed to provide consistency with the ..."
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Cited by 3 (3 self)
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Compressiveprojection principal component analysis reconstructs vectors from random projections by recovering an approximation to the principal eigenvectors of the principalcomponent transform. A heuristic for the number of eigenvectors to approximate is developed to provide consistency with the JohnsonLindenstrauss lemma and the restricted isometry property from compressedsensing theory. The resulting heuristic is driven by only quantities known at the reconstruction side of the system. The heuristic is evaluated empirically for hyperspectral imagery and is demonstrated to provide nearoptimal reconstruction quality. Index Terms—CPPCA, dimensionality reduction, random projection, hyperspectral data 1.
TreeStructured Feature Extraction Using Mutual Information
"... Abstract — One of the most informative measures for feature extraction (FE) is mutual information (MI). In terms of MI, the optimal FE creates new features that jointly have the largest dependency on the target class. However, obtaining an accurate estimate of a highdimensional MI as well as optimi ..."
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Abstract — One of the most informative measures for feature extraction (FE) is mutual information (MI). In terms of MI, the optimal FE creates new features that jointly have the largest dependency on the target class. However, obtaining an accurate estimate of a highdimensional MI as well as optimizing with respect to it is not always easy, especially when only small training sets are available. In this paper, we propose an efficient treebased method for FE in which at each step a new feature is created by selecting and linearly combining two features such that the MI between the new feature and the class is maximized. Both the selection of the features to be combined and the estimation of the coefficients of the linear transform rely on estimating 2D MIs. The estimation of the latter is computationally very efficient and robust. The effectiveness of our method is evaluated on several realworld data sets. The results show that the classification accuracy obtained by the proposed method is higher than that achieved by other FE methods. Index Terms — Classification, dimensionality reduction, feature extraction, mutual information.
Reconstruction of Hyperspectral Imagery From Random Projections Using Multihypothesis Prediction
"... Abstract—Reconstruction of hyperspectral imagery from spectral random projections is considered. Specifically, multiple predictions drawn for a pixel vector of interest are made from spatially neighboring pixel vectors within an initial nonpredicted reconstruction. A twophase hypothesisgenerat ..."
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Abstract—Reconstruction of hyperspectral imagery from spectral random projections is considered. Specifically, multiple predictions drawn for a pixel vector of interest are made from spatially neighboring pixel vectors within an initial nonpredicted reconstruction. A twophase hypothesisgeneration procedure based on partitioning and merging of spectral bands according to the correlation coefficients between bands is proposed to finetune the hypotheses. The resulting prediction is used to generate a residual in the projection domain. This residual being typically more compressible than the original pixel vector leads to improved reconstruction quality. To appropriately weight the hypothesis predictions, a distanceweighted Tikhonov regularization to an illposed leastsquares optimization is proposed. Experimental results demonstrate that the proposed reconstruction significantly outperforms alternative strategies not employing multihypothesis prediction. Index Terms—Compressed sensing, hyperspectral data, multihypothesis prediction, principal component analysis, Tikhonov regularization. I.