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Uniform Uncertainty Principle and signal recovery via Regularized Orthogonal Matching Pursuit
, 2007
"... This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantage ..."
N.TomczakJaegermann , Uniform uncertainty principle for Bernoulli and subgaussian ensembles
 Constr. Approx
"... In [CT1] Candes and Tao studied problems of approximate and exact reconstruction of sparse signals from incomplete random measurements and related them to the eigenvalue behavior of submatrices of matrices of random ..."
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Cited by 99 (6 self)
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In [CT1] Candes and Tao studied problems of approximate and exact reconstruction of sparse signals from incomplete random measurements and related them to the eigenvalue behavior of submatrices of matrices of random
Uncertainty principles and ideal atomic decomposition
 IEEE Transactions on Information Theory
, 2001
"... Suppose a discretetime signal S(t), 0 t<N, is a superposition of atoms taken from a combined time/frequency dictionary made of spike sequences 1ft = g and sinusoids expf2 iwt=N) = p N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every d ..."
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Cited by 588 (19 self)
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Suppose a discretetime signal S(t), 0 t<N, is a superposition of atoms taken from a combined time/frequency dictionary made of spike sequences 1ft = g and sinusoids expf2 iwt=N) = p N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every discretetime signal can be represented as a superposition of spikes alone, or as a superposition of sinusoids alone, there is no unique way of writing S as a sum of spikes and sinusoids in general. We prove that if S is representable as a highly sparse superposition of atoms from this time/frequency dictionary, then there is only one such highly sparse representation of S, and it can be obtained by solving the convex optimization problem of minimizing the `1 norm of the coe cients among all decompositions. Here \highly sparse " means that Nt + Nw < p N=2 where Nt is the number of time atoms, Nw is the number of frequency atoms, and N is the length of the discretetime signal.
The Dantzig Selector: Statistical Estimation When p Is Much Larger Than n
, 2007
"... In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Xβ + z, where β ∈ Rp is a parameter vector of interest, X is a data matrix with possibly far fewer rows than columns, n ≪ p ..."
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Cited by 877 (14 self)
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, where r is the residual vector y − X ˜β and t is a positive scalar. We show that if X obeys a uniform uncertainty principle (with unitnormed columns) and if the true parameter vector β is sufficiently sparse (which here roughly guarantees that the model is identifiable), then with very large
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 1400 (17 self)
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in this paper improve on our earlier work [5]. Finally, underlying the success of ℓ1 is a crucial property we call the uniform uncertainty principle that we shall describe in detail.
Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information
, 2006
"... This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discretetime signal and a randomly chosen set of frequencies. Is it possible to reconstruct from the partial knowledge of its Fourier coefficients on the set? A typical result of this pa ..."
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Cited by 2599 (51 self)
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This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discretetime signal and a randomly chosen set of frequencies. Is it possible to reconstruct from the partial knowledge of its Fourier coefficients on the set? A typical result of this paper is as follows. Suppose that is a superposition of spikes @ Aa @ A @ A obeying @�� � A I for some constant H. We do not know the locations of the spikes nor their amplitudes. Then with probability at least I @ A, can be reconstructed exactly as the solution to the I minimization problem I aH @ A s.t. ” @ Aa ” @ A for all
Advances in Prospect Theory: Cumulative Representation of Uncertainty
 JOURNAL OF RISK AND UNCERTAINTY, 5:297323 (1992)
, 1992
"... We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows differ ..."
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Cited by 1603 (12 self)
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different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a
Principled design of the modern web architecture
 ACM Trans. Internet Techn
"... The World Wide Web has succeeded in large part because its software architecture has been designed to meet the needs of an Internetscale distributed hypermedia system. The modern Web architecture emphasizes scalability of component interactions, generality of interfaces, independent deployment of c ..."
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Cited by 507 (14 self)
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of the Hypertext Transfer Protocol and Uniform Resource Identifiers. We describe the software engineering principles guiding REST and the interaction constraints chosen to retain those principles, contrasting them to the constraints of other architectural styles. We then compare the abstract model to the currently
Ontologies: Principles, methods and applications
 KNOWLEDGE ENGINEERING REVIEW
, 1996
"... This paper is intended to serve as a comprehensive introduction to the emerging field concerned with the design and use of ontologies. We observe that disparate backgrounds, languages, tools, and techniques are a major barrier to effective communication among people, organisations, and/or software s ..."
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Cited by 570 (3 self)
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This paper is intended to serve as a comprehensive introduction to the emerging field concerned with the design and use of ontologies. We observe that disparate backgrounds, languages, tools, and techniques are a major barrier to effective communication among people, organisations, and/or software systems. We show how the development and implementation of an explicit account of a shared understanding (i.e. an `ontology') in a given subject area, can improve such communication, which in turn, can give rise to greater reuse and sharing, interoperability, and more reliable software. After motivating their need, we clarify just what ontologies are and what purposes they serve. We outline a methodology for developing and evaluating ontologies, first discussing informal techniques, concerning such issues as scoping, handling ambiguity, reaching agreement and producing de nitions. We then consider the bene ts of and describe, a more formal approach. We revisit the scoping phase, and discuss the role of formal languages and techniques in the specification, implementation and evaluation of ontologies. Finally, we review the state of the art and practice in this emerging field,
Blind Signal Separation: Statistical Principles
, 2003
"... Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mut ..."
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Cited by 522 (4 self)
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, to show how they stem from basic principles and how they relate to each other.
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