A. Cohen, I. Daubechies, and J. C. Feauveau. Biorthogonal bases of compactly supported wavelets. Comm. Pure Applied Math., 1992. Home/Search Document Not in Database Summary Related Articles Check |
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Compactly Supported (bi)orthogonal Wavelets - Generated By Interpolatory (Correct)
....of compactly supported interpolatory orthonormal refinable function with dilation factor 3 were given in [BDS] Both examples in [CL] and [BDS] are continuous. Examples in [CL] are not interpolatory, while examples in [BDS] are not symmetric. Biorthogonal wavelet theory was established in [CDF] and [CD] Methods of constructions of biorthogonal wavelets were also given in [CDF] Here we focus on constructions of dual refinable functions from given interpolatory refinable functions. In [Sw] a lifting scheme was used to construct a dual mask a to the mask a of an given ....
....factor 3 were given in [BDS] Both examples in [CL] and [BDS] are continuous. Examples in [CL] are not interpolatory, while examples in [BDS] are not symmetric. Biorthogonal wavelet theory was established in [CDF] and [CD] Methods of constructions of biorthogonal wavelets were also given in [CDF]. Here we focus on constructions of dual refinable functions from given interpolatory refinable functions. In [Sw] a lifting scheme was used to construct a dual mask a to the mask a of an given interpolatory refinable function. The dual mask constructed satisfies (1:4) a( a ( a( ....
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A. Cohen, I. Daubechies and J. Feauveau, Bi-orthogonal bases of compactly supported wavelets, Comm. Pure. Appl. Math, Vol. 45 (1992), 485-560.
National Aeronautics and Space Administration Langley.. - Nasa Cr- Icase (1998) (5 citations) (Correct)
....invariant, then # j can be built to have the same property. This will be always implicitly assumed. Example . Throughout the paper, we shall illustrate our construction of matched scaling functions and wavelets starting from biorthogonal spline wavelets on the real line, as introduced in [8]. The corresponding multiresolutions on the interval are built as in [11, 12] with the choice of parameters L =2and L =4,using SVD for the biorthogonalization. The particular implementation used to produce the pictures of the present paper is described in [3] Figures 2.1 and 2.2 show the primal ....
....using the matching coe#cients given in the paper at any interface among subdomains. Refinement coe#cients. Let us start with the refinement coe#cients on the real line corresponding to the equations a k #(2x k) #(x) 2 1 2 a k #(2x where the coe#cients here are given by ([8]) a 1 =5.000000000000e 01,a 0 =1.000000000000e 00,a 1 =5.000000000000e for the primal scaling function, and by 01, a0 =1.406250000000e 00, a1 =5.937500000000e a2 = 01, a3 = 02, a4 =4.687500000000e for the dual one. Next, we give the entries of the refinement ....
[Article contains additional citation context not shown here]
A. Cohen, I. Daubechies, and J.--C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 45 (1992), pp. 485--560.
The Leveraged Wavelets and Galerkin-Wavelets Methods - Chen, Shann, Tzeng (Correct)
....and (2) Phi (x) are orthogonal to each other. It is also very interesting to realize that, as a by product, the leverage scheme and the lifting scheme of Sweldens [15] can work together to re produce all of the compactly supported biorthogonal wavelets by Cohen, Daubechies and Feauveau [5]. This procedure shall also give us a better understanding of these useful wavelets. We will demonstrate this phenomenon in Section 4. The rest of this section is devoted to a brief background explanation on why we choose this approach to the application of wavelets for numerical solution of ....
....asymptotically p when p is large. If OE(x) is not an orthonormal scaling function, there are mainly two ways to construct the (more generalized) associated wavelets. One is the semi orthogonal approach by Chui and Wang [4] another is the biorthogonal approach by Cohen, Daubechies and Feauveau [5]. Both of them use the B splines as the (non orthonormal) scaling functions. We will follow the biorthogonal approach. Let OE(x) be a scaling function which generates an MRA fV j g, and OE(x) be another scaling function which generates another MRA f V j g. More precisely, fOE(x Gamma k)g is ....
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A. Cohen, I. Daubechies and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 45 (1992), pp. 485--560.
RWTH Aachen - Titus Barsch Karsten (Correct)
....to the derived class. Figure 1 illustrates the dependencies of the different classes in MatLib. MatLib also includes the class polynom representing polynomials of finite degree: they are mainly used for the computation of the refinement coefficients for the cardinal B splines and their duals, CDF92] Finally, the class precond serves as a general framework for preconditioners in iterative methods. It only provides the abstract name; the implementation of specific preconditioners has to be done by the user. Tmatrix polynom precond Tarray2 Tsparse basematrix blbandbl blband symspa ....
....of often used refinable functions. B Splines and their duals. Function N, Nt (File trialfun.h) Syntax: Mask M = N(i) Mask M = Nt(i,j) Input: int i order 1 i 20 int j order of dual 1 j 10, i j even Description: Computes the masks of cardinal B splines and their duals constructed in [CDF92] Orthogonal Daubechies scaling functions. Function Dau (File trialfun.h) Syntax: Mask M = Dau2( Mask M = Dau3( Description: Daubechies generators. Box Splines. New tensorproduct multivariate scaling functions. Function M (File trialfun.h) Syntax: Mask M = M221( Mask M = M222( ....
A. Cohen, I. Daubechies, and J. Feauveau. Bi--orthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math., 45:485--560, 1992.
Error Estimate Of A Subdivision Scheme With A Truncated Refinement.. - Han (1997) (1 citation) (Correct)
....are used to construct smooth curves and surfaces. The reader is referred to [4, 12, 13, 16, 20, 21] for detailed discussion on interpolatory subdivision schemes and their applications to generate curves and surfaces. They are also known as scaling functions in the wavelet theory, for example, see [3, 5, 6, 8, 9, 19, 22]. This note is concerned with the behavior of a re nable function where there is a small perturbation of its re nement mask. In applications, under many situations, we need to truncate the re nement mask even though they have nite support. For example, the coecients in the re nement masks of ....
A. Cohen, I. Daubechies, and J. C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure and Appl. Math. 45 (1992), 485-560.
On Dual Wavelet Tight Frames - Han (1995) (6 citations) (Correct)
.... conditions, there is no function in H (IR) cf. 1] In Han [10] also cf. 1,3,16,17] it is proved that under certain decay conditions, if (IR) then can be obtained from a Multiresolution Analysis(MRA) For the concept of a multiresolution analysis, the reader is referred to [7,8,9,12,13,18,21]. In this paper we will give an example to show that there is a function , whose Fourier transform is positive, compactly supported and in nitely di erentiable, which generates a non MRA wavelet tight frame in H (IR) The de nition of a non Multiresolution Analysis (non MRA) wavelet tight frame ....
....of results have been obtained in the current literature. For example, Daubechies constructed many compactly supported wavelets in L (IR) in [8] Bonami, Soria and Weiss characterized band limited wavelets in [3] and many properties of wavelet frames are obtained by Chui and Shi in [4, 5] In [7], many examples of compactly supported biorthogonal wavelet bases in L (IR) are given. After reading these and other papers, we give a relatively uni ed approach to DWTFs. In this section, we shall characterize DWTFs and discuss the relation between DWTFs and biorthogonal wavelet bases. We ....
Cohen A., I. Daubechies and J.C. Feauveau, Biorthogonal Bases of Compactly Supported Wavelets. Comm. Pure Appl. Math. 45(1992), pp 485-560.
A Tutorial on Modern Lossy Wavelet Image Compression.. - Usevitch (2000) (5 citations) (Correct)
....filters, h = 11, g = 11 [3] The lack of linear phase filters in orthogonal wavelets led to research in extending wavelet analysis to more general forms, which would allow for linear phase filters. The research resulted in a more general form of wavelets known as biorthogonal wavelets [4], 5] As the name implies, biorthogonal wavelets have some orthogonality relationships between their filters. But biorthogonal wavelets differ from orthogonal in that the forward wavelet transform is equivalent to projecting the input signal on to nonorthogonal basis functions. The orthogonal and ....
A. Cohen, I. Daubechies, and J. Feauveau, "Biorthogonal bases of compactly supported wavelets," AT&T Bell Labs., Tech. Rep. 2087.
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A. Cohen, I. Daubechies, and J. C. Feauveau. Biorthogonal bases of compactly supported wavelets. Comm. Pure Applied Math., 1992.
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A. Cohen, I.Daubechies, and J.C. Feauveau. Biorthogonal Bases of Compactly Supported Wavelets. Comm. in Pure and Applied Math., 1992.
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A. Cohen, I.Daubechies, and J.C. Feauveau. Biorthogonal Bases of Compactly Supported Wavelets. Comm. in Pure and Applied Math., 1992.
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A. Cohen, I. Daubechies, and J. C. Feauveau. Biorthogonal bases of compactly supported wavelets. Comm. Pure Applied Math., 1992.
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A. Cohen, I. Daubechies, and J. C. Feauveau. Biorthogonal bases of compactly supported wavelets. Comm. Pure Applied Math., 1992.
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A. Cohen, I. Daubechies, and J. Feauveau. Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math., 45:485-560, 1992.
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A. Cohen, I. Daubechies, and J. Feauveau, \Bi-orthogonal bases of compactly supported wavelets," Comm. Pure Appl. Math. 45, pp. 485-560, 1992.
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Cohen, A., Daubechies, I., and Feauveau, J. (1992). Bi-orthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math., 45:485-560.
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A. Cohen, I. Daubechies and J.-C. Feauveau, "Biorthogonal Bases of Compactly Supported Wavelets", Comm. on Pure and Appl. Math., Vol. 45, pp. 485-560, 1992.
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A. Cohen, I. Daubechies, and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 45 (1992), pp. 485--560.
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A. Cohen, I. Daubechies and J. C. Feauveau, Bi-orthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 45 (1992) 485--560.
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A. Cohen, I. Daubechies, and J.-C. Feauveau, "Biorthogonal bases of compactly supported wavelets," Commun. Pure Appl. Math., vol. 45, pp. 485--560, 1992.
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A. Cohen, I. Daubechies, and J. C. Feauveau, "Biorthogonal bases of compactly supported wavelets", Communications on Pure and Applied Mathematics, vol. 45, pp. 485--560, 1992.
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A. Cohen, I. Daubechies and J.C. Feauveau. Biorthogonal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics, vol. 45, pp. 485--560, 1992.
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A. Cohen, I. Daubechies, and J. C. Feauveau, "Biorthogonal bases of compactly supported wavelets", Communications on Pure and Applied Mathematics, vol. 45, pp. 485--560, 1992.
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A. Cohen, I. Daubechies, and J. C. Feauveau, "Biorthogonal bases of compactly supported wavelets," Commun. Pure Appl. Math., vol. 45, pp. 485--560, 1992.
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A.Cohen, I. Daubechies, and J.-C. Feauveau, "Biorthogonal Bases of Compactly Supported Wavelets", Comm. Pure Appl. Math., Vol 45, 1992, pp. 485-560.
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A. Cohen, I. Daubechies, and J.-C. Feauveau. Biorthogonal bases of compactly supported wavelets. Commun. on Pure and Appl. Math., 45:485--560, 1992.
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A. Cohen, I. Daubechies, and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 45 (1992), 485--560.
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A. Cohen, I. Daubechies and J.C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 45 (1992), 485-560.
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A. Cohen, I. Daubechies, and J.-C. Feauveau. Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math., XIV:485--560, 1992.
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A. Cohen, I. Daubechies and J.C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 45 (1992), 485-560.
Unknown - Wenjie Hey And (Correct)
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A. Cohen, I. Daubechies, J.-C. Feauveau, Biorthogonal Bases of Compactly Supported Wavelets, Communications Pure Appl. Math. Vol. XLV(1992), 485-560.
Wavelet Deblurring Algorithms for Spatially Varying Blur.. - Chan, Chan, Shen, Shen (2002) (Correct)
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A. Cohen, I. Daubechies, and J. Feauveau, Biorthogonal Bases of Compactly Supported Wavelets, Comm. Pure Appl. Math., 45 (1992), 485-500.
A global method for invertible integer DCT and integer wavelet.. - Plonka (Correct)
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A. Cohen, I. Daubechies and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Commun. Pure Appl. Math. 45 (1992), 485-560.
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A. Cohen, I. Daubechies and J. C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 45 (1992), 485-560.
Projectable Multivariate Refinable Functions and Biorthogonal.. - Han (2002) (Correct)
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A. Cohen, I. Daubechies and J.C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 45 (1992), 485-560.
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A. Cohen, I. Daubechies e J. Feauveau, Biorthogonal bases of compactly supported wavelet, Comm. Pure Appl. Math., 45 (1992), 485-560.
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A. Cohen, I. Daubechies, and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math., 45 (1992), pp. 485-560.
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A. Cohen, I. Daubechies, and J. C. Feauveau, "Biorthogonal bases of compactly supported wavelets," Tech. Memo. number 11217-900529-07, AT&T Bell Labs.; to appear in Comm. Pure Applied Math. 23
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Cohen, A., I. Daubechies and J. C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. in Pure. and Applied Math., Vol. 45, 1992, pp. 485--560.
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