Abstract: Many real world data sets exhibit an embedding of low-dimensional structure in a high-d... more Abstract: Many real world data sets exhibit an embedding of low-dimensional structure in a high-dimensional manifold. Examples include images, videos and internet traffic data. It is of great significance to reduce the storage requirements and computational complexity when the data dimension is high. Therefore we consider the problem of reconstructing a data stream from a small subset of its entries, where the data is assumed to lie in a low-dimensional linear subspace, possibly corrupted by noise.
Abstract The theory of compressed sensing suggests that successful inversion of an image of the p... more Abstract The theory of compressed sensing suggests that successful inversion of an image of the physical world (broadly defined to include speech signals, radar/sonar returns, vibration records, sensor array snapshot vectors, 2-D images, and so on) for its source modes and amplitudes can be achieved at measurement dimensions far lower than what might be expected from the classical theories of spectrum or modal analysis, provided that the image is sparse in an apriori known basis.
Abstract We consider the problem of reconstructing a data stream from a small subset of its entri... more Abstract We consider the problem of reconstructing a data stream from a small subset of its entries, where the data stream is assumed to lie in a low-dimensional linear subspace, possibly corrupted by noise. It is also important to track the change of underlying subspace for many applications. This problem can be viewed as a sequential low-rank matrix completion problem in which the subspace is learned in an online fashion.
ABSTRACT The challenge of Multiuser Detection (MUD) is that of demodulating mutually interfering ... more ABSTRACT The challenge of Multiuser Detection (MUD) is that of demodulating mutually interfering signals given that at any time instant the number of active users is typically small. The promise of compressed sensing is the demodulation of sparse superpositions of signature waveforms from very few measurements. This paper considers signature waveforms that are are drawn from a Gabor frame.
Abstract: In this paper, we present coherence-based performance guarantees of Orthogonal Matching... more Abstract: In this paper, we present coherence-based performance guarantees of Orthogonal Matching Pursuit (OMP) for both support recovery and signal reconstruction of sparse signals when the measurements are corrupted by noise. In particular, two variants of OMP either with known sparsity level or with a stopping rule are analyzed.
Abstract: Many real world data sets exhibit an embedding of low-dimensional structure in a high-d... more Abstract: Many real world data sets exhibit an embedding of low-dimensional structure in a high-dimensional manifold. Examples include images, videos and internet traffic data. It is of great significance to reduce the storage requirements and computational complexity when the data dimension is high. Therefore we consider the problem of reconstructing a data stream from a small subset of its entries, where the data is assumed to lie in a low-dimensional linear subspace, possibly corrupted by noise.
Abstract The theory of compressed sensing suggests that successful inversion of an image of the p... more Abstract The theory of compressed sensing suggests that successful inversion of an image of the physical world (broadly defined to include speech signals, radar/sonar returns, vibration records, sensor array snapshot vectors, 2-D images, and so on) for its source modes and amplitudes can be achieved at measurement dimensions far lower than what might be expected from the classical theories of spectrum or modal analysis, provided that the image is sparse in an apriori known basis.
Abstract We consider the problem of reconstructing a data stream from a small subset of its entri... more Abstract We consider the problem of reconstructing a data stream from a small subset of its entries, where the data stream is assumed to lie in a low-dimensional linear subspace, possibly corrupted by noise. It is also important to track the change of underlying subspace for many applications. This problem can be viewed as a sequential low-rank matrix completion problem in which the subspace is learned in an online fashion.
ABSTRACT The challenge of Multiuser Detection (MUD) is that of demodulating mutually interfering ... more ABSTRACT The challenge of Multiuser Detection (MUD) is that of demodulating mutually interfering signals given that at any time instant the number of active users is typically small. The promise of compressed sensing is the demodulation of sparse superpositions of signature waveforms from very few measurements. This paper considers signature waveforms that are are drawn from a Gabor frame.
Abstract: In this paper, we present coherence-based performance guarantees of Orthogonal Matching... more Abstract: In this paper, we present coherence-based performance guarantees of Orthogonal Matching Pursuit (OMP) for both support recovery and signal reconstruction of sparse signals when the measurements are corrupted by noise. In particular, two variants of OMP either with known sparsity level or with a stopping rule are analyzed.
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