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ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
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Cited by 2684 (61 self)
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The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods
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 575 (20 self)
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/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
Perturbations of Banach Frames and Atomic Decompositions
 MATH. NACHR. 185 (1997), 33–47
, 1997
"... Banach frames and atomic decompositions are sequences that have basislike properties but which need not be bases. In particular, they allow elements of a Banach space to be written as linear combinations of the frame or atomic decomposition elements in a stable manner. In this paper we prove sever ..."
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Cited by 43 (9 self)
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Banach frames and atomic decompositions are sequences that have basislike properties but which need not be bases. In particular, they allow elements of a Banach space to be written as linear combinations of the frame or atomic decomposition elements in a stable manner. In this paper we prove
Atomic decompositions of audio signals
 in Proceedings of the IEEE ASSP Workshop on Applications of Signal Processing to Audio and Acoustics
, 1997
"... Signal modeling techniques ranging from basis expansions to parametric approaches have been applied to audio signal processing. Motivated by the fundamental limitations of basis expansions for representing arbitrary signal features and providing means for signal modifications, we consider decomposit ..."
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Cited by 5 (2 self)
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decompositions in terms of functions that are both signaladaptive and parametric in nature. Granular synthesis and sinusoidal modeling can be viewed in this light; we interpret these approaches as signaladaptive expansions in terms of timefrequency atoms that are highly correlated to the fundamental signal
ON THE ATOMIC DECOMPOSITION OF Hl AND INTERPOLATION
"... In [1] Coifman used the FeffermanStein theory of Hp spaces [4] to decompose the functions of these spaces into basic building blocks (atoms), further clarifying their real variable nature. Coifman and Weiss have provided a comprehensive treatment of these ideas and many applications to harmonic ana ..."
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In [1] Coifman used the FeffermanStein theory of Hp spaces [4] to decompose the functions of these spaces into basic building blocks (atoms), further clarifying their real variable nature. Coifman and Weiss have provided a comprehensive treatment of these ideas and many applications to harmonic
DUALITY, REFLEXIVITY AND ATOMIC DECOMPOSITIONS IN BANACH SPACES
"... Abstract. We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of “shrinking ” and “boundedly complete ” Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when ..."
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Cited by 1 (0 self)
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Abstract. We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of “shrinking ” and “boundedly complete ” Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question
Atomic decompositions and operators on Hardy spaces
 Rev. Un. Mat. Argentina
"... Abstract. This paper is essentially the second author’s lecture at the CIMPA School. It summarises large parts of the three authors ’ paper [MSV]. Only one proof is given. In the setting of a Euclidean space, we consider operators defined and uniformly bounded on atoms of a Hardy space Hp. The quest ..."
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Cited by 5 (1 self)
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. The question discussed is whether such an operator must be bounded on Hp. This leads to a study of the difference between countable and finite atomic decompositions in Hardy spaces. 1. Introduction and
ATOMIC DECOMPOSITIONS FOR TENSOR PRODUCTS AND POLYNOMIAL SPACES
"... Abstract. We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provid ..."
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Cited by 1 (1 self)
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Abstract. We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition pro
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