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On Dual Wavelet Tight Frames
 Appl. Comput. Harmon. Anal
"... . A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton's result on wavelet tight frames in L 2 (IR) is generalized to the ndimensional case. Two ways of constructing certain dual wavelet tight frame ..."
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Cited by 71 (35 self)
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. A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton's result on wavelet tight frames in L 2 (IR) is generalized to the ndimensional case. Two ways of constructing certain dual wavelet tight
Tight frames and their symmetries
 Constr. Approx
, 2005
"... The aim of this paper is to investigate symmetry properties of tight frames, with a view to constructing tight frames of orthogonal polynomials in several variables which share the symmetries of the weight function, and other similar applications. This is achieved by using representation theory to g ..."
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Cited by 34 (8 self)
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The aim of this paper is to investigate symmetry properties of tight frames, with a view to constructing tight frames of orthogonal polynomials in several variables which share the symmetries of the weight function, and other similar applications. This is achieved by using representation theory
Prime tight frames
 Adv. Comput. Math
"... Abstract: We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. We show that any finite tight frame can be written as a union of prime tight frames. We then characterize all prime harmonic tight frames as well as all prime frames constr ..."
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Cited by 5 (1 self)
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Abstract: We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. We show that any finite tight frame can be written as a union of prime tight frames. We then characterize all prime harmonic tight frames as well as all prime frames
Localized tight frames on spheres
 SIAM J. Math. Anal
, 2006
"... Abstract. In this paper we wish to present a new class of tight frames on the sphere. These frames have excellent pointwise localization and approximation properties. These properties are based on pointwise localization of kernels arising in the spectral calculus for certain selfadjoint operators, ..."
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Cited by 77 (11 self)
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Abstract. In this paper we wish to present a new class of tight frames on the sphere. These frames have excellent pointwise localization and approximation properties. These properties are based on pointwise localization of kernels arising in the spectral calculus for certain selfadjoint operators
Isometric tight frames
 Electr. J. Lin. Algeb
, 2002
"... Abstract. A d × n matrix, n ≥ d, whose columns have equal length and whose rows are orthonormal is constructed. This is equivalent to finding an isometric tight frame of n vectors in R d (or C d), or writing the d × d identity matrix I = d ∑n n i=1 Pi, wherethePiare rank 1 orthogonal projections. Th ..."
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Cited by 2 (0 self)
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Abstract. A d × n matrix, n ≥ d, whose columns have equal length and whose rows are orthonormal is constructed. This is equivalent to finding an isometric tight frame of n vectors in R d (or C d), or writing the d × d identity matrix I = d ∑n n i=1 Pi, wherethePiare rank 1 orthogonal projections
Uniform Tight Frames with Erasures
"... Uniform tight frames have beenshown to be useful for robust data transmission. The losses in the network are modeled as erasures of transmitted frame coe cients. We give the first systematic study of the general class of uniform tight frames and their properties. We search for efficient construction ..."
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Cited by 8 (1 self)
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Uniform tight frames have beenshown to be useful for robust data transmission. The losses in the network are modeled as erasures of transmitted frame coe cients. We give the first systematic study of the general class of uniform tight frames and their properties. We search for efficient
On the existence of equiangular tight frames
 Linear Algebra Appl
, 2004
"... In a recent paper, Holmes and Paulsen established a necessary condition for the existence of an Nvector equiangular tight frame in a ddimensional real Euclidean space. This article develops much stronger necessary conditions using a combination of field theory and graph theory. This investigation ..."
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Cited by 21 (1 self)
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In a recent paper, Holmes and Paulsen established a necessary condition for the existence of an Nvector equiangular tight frame in a ddimensional real Euclidean space. This article develops much stronger necessary conditions using a combination of field theory and graph theory. This investigation
New tight frames of curvelets and optimal representations of objects with piecewise C² singularities
 COMM. ON PURE AND APPL. MATH
, 2002
"... This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges. Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needleshap ..."
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Cited by 428 (21 self)
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This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges. Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needle
Lapped tight frame transforms
 in Proc. IEEE Int. Conf. Acoust., Speech and Signal Proc
"... We propose a new class of equalnorm tight frames termed Lapped Tight Frame Transforms (LTFTs). These can be seen as a redundant counterpart to bases known as Lapped Orthogonal Transforms (LOTs) introduced by Malvar and Cassereau, as well as an in¿nitedimensional counterpart to Harmonic Tight Fram ..."
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Cited by 7 (3 self)
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We propose a new class of equalnorm tight frames termed Lapped Tight Frame Transforms (LTFTs). These can be seen as a redundant counterpart to bases known as Lapped Orthogonal Transforms (LOTs) introduced by Malvar and Cassereau, as well as an in¿nitedimensional counterpart to Harmonic Tight
ELA ISOMETRIC TIGHT FRAMES∗
"... Abstract. A d × n matrix, n ≥ d, whose columns have equal length and whose rows are orthonormal is constructed. This is equivalent to finding an isometric tight frame of n vectors in R d (or C ..."
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Abstract. A d × n matrix, n ≥ d, whose columns have equal length and whose rows are orthonormal is constructed. This is equivalent to finding an isometric tight frame of n vectors in R d (or C
Results 1  10
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973