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Guaranteed Sparse Recovery under Linear Transformation
"... We consider the following signal recovery problem: given a measurement matrix Φ ∈ R n×p and a noisy observation vector c ∈ R n constructed from c = Φθ ∗ + ɛ where ɛ ∈ R n is the noise vector whose entries follow i.i.d. centered subGaussian distribution, how to recover the signal θ ∗ if Dθ ∗ is spar ..."
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Cited by 2 (0 self)
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∗ is sparse under a linear transformation D ∈ R m×p? One natural method using convex optimization is to solve the following problem: min θ 1 2 ‖Φθ − c‖2 + λ‖Dθ‖1. This paper provides an upper bound of the estimate error and shows the consistency property of this method by assuming that the design matrix Φ
KSVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
, 2006
"... In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signalatoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and inc ..."
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Cited by 925 (40 self)
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by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse
Decoding by Linear Programming
, 2004
"... This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to rec ..."
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Cited by 1371 (16 self)
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for some ρ> 0. In short, f can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program). In addition, numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 478 (2 self)
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that convex relaxation succeeds. As evidence of the broad impact of these results, the paper describes how convex relaxation can be used for several concrete signal recovery problems. It also describes applications to channel coding, linear regression, and numerical analysis.
Understanding FaultTolerant Distributed Systems
 COMMUNICATIONS OF THE ACM
, 1993
"... We propose a small number of basic concepts that can be used to explain the architecture of faulttolerant distributed systems and we discuss a list of architectural issues that we find useful to consider when designing or examining such systems. For each issue we present known solutions and design ..."
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Cited by 374 (23 self)
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We propose a small number of basic concepts that can be used to explain the architecture of faulttolerant distributed systems and we discuss a list of architectural issues that we find useful to consider when designing or examining such systems. For each issue we present known solutions and design alternatives, we discuss their relative merits and we give examples of systems which adopt one approach or the other. The aim is to introduce some order in the complex discipline of designing and understanding faulttolerant distributed systems.
Sparse phase retrieval: Uniqueness guarantees and recovery algorithms
, 2013
"... The problem of signal recovery from its Fourier transform magnitude, or equivalently, autocorrelation, is of paramount importance in various fields of engineering and has been around for over 100 years. In order to achieve this, additional structure information about the signal is necessary. In thi ..."
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Cited by 1 (0 self)
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. In this work, we first provide simple and general conditions, which when satisfied, allow unique recovery almost surely. In particular, we focus our attention on sparse signals and show that most O(n)sparse signals, i.e., signals with O(n) nonzero components, have distinct Fourier transform magnitudes (up
DOUBLY SPARSE TRANSFORM LEARNINGWITH CONVERGENCE GUARANTEES
"... The sparsity of natural signals in transform domains such as the DCT has been heavily exploited in various applications. Recently, we introduced the idea of learning sparsifying transforms from data, and demonstrated the usefulness of learnt transforms in image representation, and denoising. Howev ..."
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. However, the learning formulations therein were nonconvex, and the algorithms lacked strong convergence properties. In this work, we propose a novel convex formulation for square sparsifying transform learning. We also enforce a doubly sparse structure on the transform, which makes its learning, stor
Network Centric Warfare: Developing and Leveraging Information Superiority
 Command and Control Research Program (CCRP), US DoD
, 2000
"... the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technolo ..."
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Cited by 308 (5 self)
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the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technologies. The CCRP pursues a broad program of research and analysis in information superiority, information operations, command and control theory, and associated operational concepts that enable us to leverage shared awareness to improve the effectiveness and efficiency of assigned missions. An important aspect of the CCRP program is its ability to serve as a bridge between the operational, technical, analytical, and educational communities. The CCRP provides leadership for the command and control research community by: n n
Sparse recovery using sparse matrices
, 2008
"... We consider the approximate sparse recovery problem, where the goal is to (approximately) recover a highdimensional vector x from its lowerdimensional sketch Ax. A popular way of performing this recovery is by finding x # such that Ax = Ax # , and ‖x # ‖1 is minimal. It is known that this approach ..."
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Cited by 11 (1 self)
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We consider the approximate sparse recovery problem, where the goal is to (approximately) recover a highdimensional vector x from its lowerdimensional sketch Ax. A popular way of performing this recovery is by finding x # such that Ax = Ax # , and ‖x # ‖1 is minimal. It is known
Blocksparse signals: Uncertainty relations and efficient recovery
 IEEE TRANS. SIGNAL PROCESS
, 2010
"... We consider efficient methods for the recovery of blocksparse signals — i.e., sparse signals that have nonzero entries occurring in clusters—from an underdetermined system of linear equations. An uncertainty relation for blocksparse signals is derived, based on a blockcoherence measure, which we ..."
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Cited by 156 (17 self)
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We consider efficient methods for the recovery of blocksparse signals — i.e., sparse signals that have nonzero entries occurring in clusters—from an underdetermined system of linear equations. An uncertainty relation for blocksparse signals is derived, based on a blockcoherence measure, which
Results 1  10
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575,063