The Experts below are selected from a list of 3603 Experts worldwide ranked by ideXlab platform
Michael B Wakin - One of the best experts on this subject based on the ideXlab platform.
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the Restricted Isometry Property for random block diagonal matrices
Applied and Computational Harmonic Analysis, 2015Co-Authors: Armin Eftekhari, Han Lun Yap, Christopher J Rozell, Michael B WakinAbstract:Abstract In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. It is by now well-known that Gaussian (or, more generally, sub-Gaussian) random matrices satisfy the RIP under certain conditions on the number of measurements. Their use can be limited in practice, however, due to storage limitations, computational considerations, or the mismatch of such matrices with certain measurement architectures. These issues have recently motivated considerable effort towards studying the RIP for structured random matrices. In this paper, we study the RIP for block diagonal measurement matrices where each block on the main diagonal is itself a sub-Gaussian random matrix. Our main result states that such matrices can indeed satisfy the RIP but that the requisite number of measurements depends on certain properties of the basis in which the signals are sparse. In the best case, these matrices perform nearly as well as dense Gaussian random matrices, despite having many fewer nonzero entries.
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the Restricted Isometry Property for block diagonal matrices
Conference on Information Sciences and Systems, 2011Co-Authors: Han Lun Yap, Michael B Wakin, Armin Eftekhari, Christopher J RozellAbstract:In compressive sensing (CS), the Restricted Isometry Property (RIP) is a powerful condition on measurement operators which ensures robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. Early papers in CS showed that Gaussian random matrices satisfy the RIP with high probability, but such matrices are usually undesirable in practical applications due to storage limitations, computational considerations, or the mismatch of such matrices with certain measurement architectures. To alleviate some or all of these difficulties, recent research efforts have focused on structured random matrices. In this paper, we study block diagonal measurement matrices where each block on the main diagonal is itself a Gaussian random matrix. The main result of this paper shows that such matrices can indeed satisfy the RIP but that the requisite number of measurements depends on the coherence of the basis in which the signals are sparse. In the best case—for signals that are sparse in the frequency domain—these matrices perform nearly as well as dense Gaussian random matrices despite having many fewer nonzero entries.
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stable manifold embeddings with operators satisfying the Restricted Isometry Property
Conference on Information Sciences and Systems, 2011Co-Authors: Han Lun Yap, Michael B Wakin, Christopher J RozellAbstract:Signals of interests can often be thought to come from a low dimensional signal model. The exploitation of this fact has led to many recent interesting advances in signal processing, one notable example being in the field of compressive sensing (CS). The literature on CS has established that many matrices satisfy the Restricted Isometry Property (RIP), which guarantees a stable (i.e., distance-preserving) embedding of a sparse signal model from an undersampled linear measurement system. In this work, we study the stable embedding of manifold signal models using matrices that satisfy the RIP. We show that by paying reasonable additional factors in the number of measurements, all matrices that satisfy the RIP can also be used (in conjunction with a random sign sequence) to obtain a stable embedding of a manifold.
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CISS - Stable manifold embeddings with operators satisfying the Restricted Isometry Property
2011 45th Annual Conference on Information Sciences and Systems, 2011Co-Authors: Han Lun Yap, Michael B Wakin, Christopher J RozellAbstract:Signals of interests can often be thought to come from a low dimensional signal model. The exploitation of this fact has led to many recent interesting advances in signal processing, one notable example being in the field of compressive sensing (CS). The literature on CS has established that many matrices satisfy the Restricted Isometry Property (RIP), which guarantees a stable (i.e., distance-preserving) embedding of a sparse signal model from an undersampled linear measurement system. In this work, we study the stable embedding of manifold signal models using matrices that satisfy the RIP. We show that by paying reasonable additional factors in the number of measurements, all matrices that satisfy the RIP can also be used (in conjunction with a random sign sequence) to obtain a stable embedding of a manifold.
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CISS - The Restricted Isometry Property for block diagonal matrices
2011 45th Annual Conference on Information Sciences and Systems, 2011Co-Authors: Han Lun Yap, Michael B Wakin, Armin Eftekhari, Christopher J RozellAbstract:In compressive sensing (CS), the Restricted Isometry Property (RIP) is a powerful condition on measurement operators which ensures robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. Early papers in CS showed that Gaussian random matrices satisfy the RIP with high probability, but such matrices are usually undesirable in practical applications due to storage limitations, computational considerations, or the mismatch of such matrices with certain measurement architectures. To alleviate some or all of these difficulties, recent research efforts have focused on structured random matrices. In this paper, we study block diagonal measurement matrices where each block on the main diagonal is itself a Gaussian random matrix. The main result of this paper shows that such matrices can indeed satisfy the RIP but that the requisite number of measurements depends on the coherence of the basis in which the signals are sparse. In the best case—for signals that are sparse in the frequency domain—these matrices perform nearly as well as dense Gaussian random matrices despite having many fewer nonzero entries.
Rudolf Mathar - One of the best experts on this subject based on the ideXlab platform.
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The Group Restricted Isometry Property for Subgaussian Block Diagonal Matrices
2019 IEEE International Symposium on Information Theory (ISIT), 2019Co-Authors: Niklas Koep, Arash Behboodi, Rudolf MatharAbstract:We address the problem of reconstructing group-sparse vectors from compressive measurements acquired via subgaussian block diagonal measurement operators. Such results can be obtained by establishing the so-called group Restricted Isometry Property of the underlying measurement matrix. In particular, the problem is reduced to the task of bounding certain geometric objects associated with the suprema of a particular chaos process, which involves estimating Talagrand's γ2-functional via Dudley's metric entropy integral. As part of the proof, we generalize Maurey's empirical method to provide new bounds on the covering number of sets consisting of finite convex combinations of compact sets.
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ISIT - The Group Restricted Isometry Property for Subgaussian Block Diagonal Matrices
2019 IEEE International Symposium on Information Theory (ISIT), 2019Co-Authors: Niklas Koep, Arash Behboodi, Rudolf MatharAbstract:We address the problem of reconstructing group-sparse vectors from compressive measurements acquired via subgaussian block diagonal measurement operators. Such results can be obtained by establishing the so-called group Restricted Isometry Property of the underlying measurement matrix. In particular, the problem is reduced to the task of bounding certain geometric objects associated with the suprema of a particular chaos process, which involves estimating Talagrand’s γ 2 -functional via Dudley’s metric entropy integral. As part of the proof, we generalize Maurey’s empirical method to provide new bounds on the covering number of sets consisting of finite convex combinations of compact sets.
Christopher J Rozell - One of the best experts on this subject based on the ideXlab platform.
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the Restricted Isometry Property for random block diagonal matrices
Applied and Computational Harmonic Analysis, 2015Co-Authors: Armin Eftekhari, Han Lun Yap, Christopher J Rozell, Michael B WakinAbstract:Abstract In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. It is by now well-known that Gaussian (or, more generally, sub-Gaussian) random matrices satisfy the RIP under certain conditions on the number of measurements. Their use can be limited in practice, however, due to storage limitations, computational considerations, or the mismatch of such matrices with certain measurement architectures. These issues have recently motivated considerable effort towards studying the RIP for structured random matrices. In this paper, we study the RIP for block diagonal measurement matrices where each block on the main diagonal is itself a sub-Gaussian random matrix. Our main result states that such matrices can indeed satisfy the RIP but that the requisite number of measurements depends on certain properties of the basis in which the signals are sparse. In the best case, these matrices perform nearly as well as dense Gaussian random matrices, despite having many fewer nonzero entries.
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the Restricted Isometry Property for echo state networks with applications to sequence memory capacity
IEEE Signal Processing Workshop on Statistical Signal Processing, 2012Co-Authors: Han Lun Yap, Adam S Charles, Christopher J RozellAbstract:The ability of networked systems (including artificial or biological neuronal networks) to perform complex data processing tasks relies in part on their ability to encode signals from the recent past in the current network state. Here we use Compressed Sensing tools to study the ability of a particular network architecture (Echo State Networks) to stably store long input sequences. In particular, we show that such networks satisfy the Restricted Isometry Property when the input sequences are compressible in certain bases and when the number of nodes scale linearly with the sparsity of the input sequence and logarithmically with its dimension. Thus, the memory capacity of these networks depends on the input sequence statistics, and can (sometimes greatly) exceed the number of nodes in the network. Furthermore, input sequences can be robustly recovered from the instantaneous network state using a tractable optimization program (also implementable in a network architecture).
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the Restricted Isometry Property for block diagonal matrices
Conference on Information Sciences and Systems, 2011Co-Authors: Han Lun Yap, Michael B Wakin, Armin Eftekhari, Christopher J RozellAbstract:In compressive sensing (CS), the Restricted Isometry Property (RIP) is a powerful condition on measurement operators which ensures robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. Early papers in CS showed that Gaussian random matrices satisfy the RIP with high probability, but such matrices are usually undesirable in practical applications due to storage limitations, computational considerations, or the mismatch of such matrices with certain measurement architectures. To alleviate some or all of these difficulties, recent research efforts have focused on structured random matrices. In this paper, we study block diagonal measurement matrices where each block on the main diagonal is itself a Gaussian random matrix. The main result of this paper shows that such matrices can indeed satisfy the RIP but that the requisite number of measurements depends on the coherence of the basis in which the signals are sparse. In the best case—for signals that are sparse in the frequency domain—these matrices perform nearly as well as dense Gaussian random matrices despite having many fewer nonzero entries.
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stable manifold embeddings with operators satisfying the Restricted Isometry Property
Conference on Information Sciences and Systems, 2011Co-Authors: Han Lun Yap, Michael B Wakin, Christopher J RozellAbstract:Signals of interests can often be thought to come from a low dimensional signal model. The exploitation of this fact has led to many recent interesting advances in signal processing, one notable example being in the field of compressive sensing (CS). The literature on CS has established that many matrices satisfy the Restricted Isometry Property (RIP), which guarantees a stable (i.e., distance-preserving) embedding of a sparse signal model from an undersampled linear measurement system. In this work, we study the stable embedding of manifold signal models using matrices that satisfy the RIP. We show that by paying reasonable additional factors in the number of measurements, all matrices that satisfy the RIP can also be used (in conjunction with a random sign sequence) to obtain a stable embedding of a manifold.
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CISS - Stable manifold embeddings with operators satisfying the Restricted Isometry Property
2011 45th Annual Conference on Information Sciences and Systems, 2011Co-Authors: Han Lun Yap, Michael B Wakin, Christopher J RozellAbstract:Signals of interests can often be thought to come from a low dimensional signal model. The exploitation of this fact has led to many recent interesting advances in signal processing, one notable example being in the field of compressive sensing (CS). The literature on CS has established that many matrices satisfy the Restricted Isometry Property (RIP), which guarantees a stable (i.e., distance-preserving) embedding of a sparse signal model from an undersampled linear measurement system. In this work, we study the stable embedding of manifold signal models using matrices that satisfy the RIP. We show that by paying reasonable additional factors in the number of measurements, all matrices that satisfy the RIP can also be used (in conjunction with a random sign sequence) to obtain a stable embedding of a manifold.
Gonzalo R Arce - One of the best experts on this subject based on the ideXlab platform.
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colored coded apertures optimization in compressive spectral imaging by Restricted Isometry Property
International Conference on Image Processing, 2014Co-Authors: Henry Arguello, Yuri Mejia, Gonzalo R ArceAbstract:Coded Aperture Snapshot Spectral Imaging (CASSI) systems capture the spatial and spectral information of a scene by measuring 2D coded projections on a focal plane array (FPA). Compressed sensing reconstruction algorithms are then used to recover the underlying spectral data cube. The quality of the reconstructions in CASSI is determined by the design of a set of block-unblock coded apertures. In this work, the block-unblock coded apertures in CASSI are replaced by colored coded apertures. The Restricted Isometry Property (RIP) of the colored CASSI is developed and the structure of the colored coded apertures is designed such that the RIP is better satisfied. Simulations show significant gain in the quality of reconstructions for the optimized colored coded apertures over that attained by traditional block-unblock coded apertures.
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ICIP - Colored coded apertures optimization in compressive spectral imaging by Restricted Isometry Property
2014 IEEE International Conference on Image Processing (ICIP), 2014Co-Authors: Henry Arguello, Yuri Mejia, Gonzalo R ArceAbstract:Coded Aperture Snapshot Spectral Imaging (CASSI) systems capture the spatial and spectral information of a scene by measuring 2D coded projections on a focal plane array (FPA). Compressed sensing reconstruction algorithms are then used to recover the underlying spectral data cube. The quality of the reconstructions in CASSI is determined by the design of a set of block-unblock coded apertures. In this work, the block-unblock coded apertures in CASSI are replaced by colored coded apertures. The Restricted Isometry Property (RIP) of the colored CASSI is developed and the structure of the colored coded apertures is designed such that the RIP is better satisfied. Simulations show significant gain in the quality of reconstructions for the optimized colored coded apertures over that attained by traditional block-unblock coded apertures.
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Restricted Isometry Property in coded aperture compressive spectral imaging
IEEE Signal Processing Workshop on Statistical Signal Processing, 2012Co-Authors: Henry Arguello, Gonzalo R ArceAbstract:Coded Aperture Snapshot Spectral Imaging Systems (CASSI) capture the spectral information of a scene using a set of coded focal plane array measurements. Compressed sensing reconstruction algorithms are used to reconstruct the underlying spectral 3D data cube. The coded measurements in CASSI use structured sensing matrices. This article describes the Restricted Isometry Property (RIP) for the projection matrices used in CASSI. In turn, the RIP provides guidelines for the minimum number of FPA measurement shots needed for image reconstruction. It also provides the optimal transmittance parameters for the set of code apertures used in the acquisition process.
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SSP - Restricted Isometry Property in coded aperture compressive spectral imaging
2012 IEEE Statistical Signal Processing Workshop (SSP), 2012Co-Authors: Henry Arguello, Gonzalo R ArceAbstract:Coded Aperture Snapshot Spectral Imaging Systems (CASSI) capture the spectral information of a scene using a set of coded focal plane array measurements. Compressed sensing reconstruction algorithms are used to reconstruct the underlying spectral 3D data cube. The coded measurements in CASSI use structured sensing matrices. This article describes the Restricted Isometry Property (RIP) for the projection matrices used in CASSI. In turn, the RIP provides guidelines for the minimum number of FPA measurement shots needed for image reconstruction. It also provides the optimal transmittance parameters for the set of code apertures used in the acquisition process.
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generalized Restricted Isometry Property for alpha stable random projections
International Conference on Acoustics Speech and Signal Processing, 2011Co-Authors: Daniel Otero, Gonzalo R ArceAbstract:The Restricted Isometry Property (RIP) is an important concept in compressed sensing. It is well known that many random matrices satisfy the RIP with high probability, whenever the entries of the random matrix have finite second order moment. Recent work in compressed sensing has shown that it is possible to do dimensionality reduction and signal reconstruction using Cauchy random projections. This suggests that the l 1 distance is preserved when one projects a set of data points from a high-dimensional space, to one of lower dimension with a random matrix which does not have finite variance. This paper generalizes this concept where it is shown that α-stable projections, which preserve the l α distance, also satisfy a generalized RIP Property and consequently reconstruction from α-stable projections is feasible.
Han Lun Yap - One of the best experts on this subject based on the ideXlab platform.
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the Restricted Isometry Property for random block diagonal matrices
Applied and Computational Harmonic Analysis, 2015Co-Authors: Armin Eftekhari, Han Lun Yap, Christopher J Rozell, Michael B WakinAbstract:Abstract In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. It is by now well-known that Gaussian (or, more generally, sub-Gaussian) random matrices satisfy the RIP under certain conditions on the number of measurements. Their use can be limited in practice, however, due to storage limitations, computational considerations, or the mismatch of such matrices with certain measurement architectures. These issues have recently motivated considerable effort towards studying the RIP for structured random matrices. In this paper, we study the RIP for block diagonal measurement matrices where each block on the main diagonal is itself a sub-Gaussian random matrix. Our main result states that such matrices can indeed satisfy the RIP but that the requisite number of measurements depends on certain properties of the basis in which the signals are sparse. In the best case, these matrices perform nearly as well as dense Gaussian random matrices, despite having many fewer nonzero entries.
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the Restricted Isometry Property for echo state networks with applications to sequence memory capacity
IEEE Signal Processing Workshop on Statistical Signal Processing, 2012Co-Authors: Han Lun Yap, Adam S Charles, Christopher J RozellAbstract:The ability of networked systems (including artificial or biological neuronal networks) to perform complex data processing tasks relies in part on their ability to encode signals from the recent past in the current network state. Here we use Compressed Sensing tools to study the ability of a particular network architecture (Echo State Networks) to stably store long input sequences. In particular, we show that such networks satisfy the Restricted Isometry Property when the input sequences are compressible in certain bases and when the number of nodes scale linearly with the sparsity of the input sequence and logarithmically with its dimension. Thus, the memory capacity of these networks depends on the input sequence statistics, and can (sometimes greatly) exceed the number of nodes in the network. Furthermore, input sequences can be robustly recovered from the instantaneous network state using a tractable optimization program (also implementable in a network architecture).
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the Restricted Isometry Property for block diagonal matrices
Conference on Information Sciences and Systems, 2011Co-Authors: Han Lun Yap, Michael B Wakin, Armin Eftekhari, Christopher J RozellAbstract:In compressive sensing (CS), the Restricted Isometry Property (RIP) is a powerful condition on measurement operators which ensures robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. Early papers in CS showed that Gaussian random matrices satisfy the RIP with high probability, but such matrices are usually undesirable in practical applications due to storage limitations, computational considerations, or the mismatch of such matrices with certain measurement architectures. To alleviate some or all of these difficulties, recent research efforts have focused on structured random matrices. In this paper, we study block diagonal measurement matrices where each block on the main diagonal is itself a Gaussian random matrix. The main result of this paper shows that such matrices can indeed satisfy the RIP but that the requisite number of measurements depends on the coherence of the basis in which the signals are sparse. In the best case—for signals that are sparse in the frequency domain—these matrices perform nearly as well as dense Gaussian random matrices despite having many fewer nonzero entries.
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stable manifold embeddings with operators satisfying the Restricted Isometry Property
Conference on Information Sciences and Systems, 2011Co-Authors: Han Lun Yap, Michael B Wakin, Christopher J RozellAbstract:Signals of interests can often be thought to come from a low dimensional signal model. The exploitation of this fact has led to many recent interesting advances in signal processing, one notable example being in the field of compressive sensing (CS). The literature on CS has established that many matrices satisfy the Restricted Isometry Property (RIP), which guarantees a stable (i.e., distance-preserving) embedding of a sparse signal model from an undersampled linear measurement system. In this work, we study the stable embedding of manifold signal models using matrices that satisfy the RIP. We show that by paying reasonable additional factors in the number of measurements, all matrices that satisfy the RIP can also be used (in conjunction with a random sign sequence) to obtain a stable embedding of a manifold.
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CISS - Stable manifold embeddings with operators satisfying the Restricted Isometry Property
2011 45th Annual Conference on Information Sciences and Systems, 2011Co-Authors: Han Lun Yap, Michael B Wakin, Christopher J RozellAbstract:Signals of interests can often be thought to come from a low dimensional signal model. The exploitation of this fact has led to many recent interesting advances in signal processing, one notable example being in the field of compressive sensing (CS). The literature on CS has established that many matrices satisfy the Restricted Isometry Property (RIP), which guarantees a stable (i.e., distance-preserving) embedding of a sparse signal model from an undersampled linear measurement system. In this work, we study the stable embedding of manifold signal models using matrices that satisfy the RIP. We show that by paying reasonable additional factors in the number of measurements, all matrices that satisfy the RIP can also be used (in conjunction with a random sign sequence) to obtain a stable embedding of a manifold.
