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635
The Levering Scheme Of Biorthogonal Wavelets
 in &quot;Proceedings of International Wavelets Conference,&quot; Tangier
, 1998
"... We present a scheme that will lever orthonormal or biorthogonal wavelets to a new system of biorthogonal wavelets. If we start with orthonormal wavelets, the raised scaling functions and wavelets are compactly supported and are differentiable. The derivatives of the raised biorthogonal scaling/wavel ..."
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Cited by 4 (2 self)
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We present a scheme that will lever orthonormal or biorthogonal wavelets to a new system of biorthogonal wavelets. If we start with orthonormal wavelets, the raised scaling functions and wavelets are compactly supported and are differentiable. The derivatives of the raised biorthogonal scaling/wavelets
Biorthogonal Wavelet Expansions
 Constr. Approx
"... This paper is concerned with developing conditions on a given finite collection of compactly supported algebraically linearly independent refinable functions that insure the existence of biorthogonal systems of refinable functions with similar properties. In particular we address the close connectio ..."
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Cited by 59 (6 self)
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connection of this issue with stationary subdivision schemes. Key Words: Finiteley generated shiftinvariant spaces, stationary subdivision schemes, matrix refinement relations, biorthogonal wavelets. AMS Subject Classification: 39B62, 41A63 1 Introduction During the past few years the construction
Biorthogonal Wavelets and Multigrid
 in: Adaptive Methods  Algorithms, Theory and Applications, Proceedings of the 9th GAMM Seminar, W. Hackbusch, G. Wittum (eds.), NNFM Series
, 1994
"... We will be concerned with the solution of an elliptic boundary value problem in one dimension with polynomial coefficients. In a Galerkin approach, we employ biorthogonal wavelets adapted to a differential operator with constant coefficients, and use the refinement equations to set up the system of ..."
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Cited by 3 (2 self)
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We will be concerned with the solution of an elliptic boundary value problem in one dimension with polynomial coefficients. In a Galerkin approach, we employ biorthogonal wavelets adapted to a differential operator with constant coefficients, and use the refinement equations to set up the system
Biorthogonal Wavelets for Image Compression
, 1994
"... Biorthogonal wavelets or filterbanks are shown to be superior in coding gain performance to orthogonal ones for logarithmic subband decompositions (limited to iterative decomposition of the downsampled output of the analysis lowpass filter). As a consequence, for logarithmic decompositions, the opt ..."
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Cited by 8 (1 self)
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Biorthogonal wavelets or filterbanks are shown to be superior in coding gain performance to orthogonal ones for logarithmic subband decompositions (limited to iterative decomposition of the downsampled output of the analysis lowpass filter). As a consequence, for logarithmic decompositions
Biorthogonal wavelets for subdivision volumes
 In: Proceedings of the Seventh ACM Symposium on Solid Modeling and Applications
, 2002
"... Figure 1: Volume subdivision, manipulation, and fitting. A lattice (top left) is recursively subdivided and reshaped at the fourth subdivision level. This shape is lowpass filtered by removing fineresolution wavelet coefficients (bottom right). We present a biorthogonal wavelet construction based ..."
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Cited by 5 (0 self)
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Figure 1: Volume subdivision, manipulation, and fitting. A lattice (top left) is recursively subdivided and reshaped at the fourth subdivision level. This shape is lowpass filtered by removing fineresolution wavelet coefficients (bottom right). We present a biorthogonal wavelet construction
Biorthogonal Wavelet Space: Parametrization And Factorization
 SIAM JOURNAL ON MATHEMATICAL ANALYSIS
, 1999
"... In this paper we study the algebraic and geometric structure of the space of compactly supported biorthogonal wavelets. We prove that any biorthogonal wavelet matrix pair (which consists of the scaling filters and wavelet filters) can be factored as the product of primitive paraunitary matrices, a ..."
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Cited by 5 (0 self)
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In this paper we study the algebraic and geometric structure of the space of compactly supported biorthogonal wavelets. We prove that any biorthogonal wavelet matrix pair (which consists of the scaling filters and wavelet filters) can be factored as the product of primitive paraunitary matrices, a
Numerical stability of biorthogonal wavelet transforms
 Advances in Comp. Math
, 1995
"... Abstract. For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2norm and average 2norm of these transforms, incl ..."
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Cited by 4 (0 self)
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Abstract. For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2norm and average 2norm of these transforms
Interpolatory Biorthogonal Wavelets and CBC Algorithm
"... . In this paper, we shall discuss how to construct multidimensional biorthogonal wavelets by employing a coset by coset (CBC) algorithm. We shall construct biorthogonal wavelets on the hexagonal lattice by CBC algorithm. In particular, we shall propose a CBC algorithm to construct interpolatory bior ..."
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Cited by 1 (0 self)
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. In this paper, we shall discuss how to construct multidimensional biorthogonal wavelets by employing a coset by coset (CBC) algorithm. We shall construct biorthogonal wavelets on the hexagonal lattice by CBC algorithm. In particular, we shall propose a CBC algorithm to construct interpolatory
Stability Of Biorthogonal Wavelet Bases
, 2003
"... this paper is to develop a simpler, but equivalent, set of conditions which permit more rapid numerical testing. Towards this end we make two observations concerning condition E in the case of finite filters satisfying some minor restrictions which we elucidate below: (i) Condition E holds for a gen ..."
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Cited by 2 (2 self)
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is the observation that for real, finite filters this singleparameter reformulation of the lifting scheme generates biorthogonal filter banks having associated wavelets in L 2 (R) provided the single parameter lies in an open interval containing zero. Moreover, we provide an algorithm fo...
Biorthogonal Wavelets For Fast Matrix Computations
 Appl. Comput. Harmon. Anal
, 1994
"... . In [1], Beylkin et al. introduced a waveletbased algorithm that approximates integral or matrix operators of a certain type by highly sparse matrices, as the basis for efficient approximate calculations. The wavelets best suited for achieving the highest possible compression with this algorithm a ..."
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Cited by 8 (1 self)
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are Daubechies wavelets, while Coiflets lead to a faster decomposition algorithm at slightly lesser compression. We observe that the same algorithm can be based on biorthogonal instead of orthogonal wavelets, and derive two classes of biorthogonal wavelets that achieve high compression and high decomposition
Results 1  10
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635