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Multiwavelets
"... In many applications of image processing, the given data are integervalued. It is therefore desirable to construct transformations that map data of this type to an integer #or rational# ring. Calderbank, Daubechies, Sweldens, and Yeo #1# devised two methods for modifying orthogonal and biorthonal w ..."
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Daubechies orthogonal wavelet transform #2#. Wehave observed that this factorization can be extended to 4tap multiwavelets of arbitrary size. In this paper we will discuss this generalization and illustrate the factorization on twomultiwavelets. In particular, the wellknown Donovan, Geronimo, Hardin
From Wavelets to Multiwavelets
 in Mathematical Methods for Curves and Surfaces
, 1998
"... . This paper gives an overview of recent achievements of the multiwavelet theory. The construction of multiwavelets is based on a multiresolution analysis with higher multiplicity generated by a scaling vector. The basic properties of scaling vectors such as L 2 stability, approximation order and ..."
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Cited by 7 (1 self)
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. This paper gives an overview of recent achievements of the multiwavelet theory. The construction of multiwavelets is based on a multiresolution analysis with higher multiplicity generated by a scaling vector. The basic properties of scaling vectors such as L 2 stability, approximation order
Multiwavelets and Integer Transforms
"... In many applications of image processing, the given data are integervalued. It is therefore desirable to construct transformations that map data of this type to an integer (or rational) ring. Calderbank, Daubechies, Sweldens, and Yeo [1] devised two methods for modifying orthogonal and biorthonal w ..."
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Cited by 2 (0 self)
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Daubechies orthogonal wavelet transform [2]. We have observed that this factorization can be extended to 4tap multiwavelets of arbitrary size. In this paper we will discuss this generalization and illustrate the factorization on two multiwavelets. In particular, the wellknown Donovan, Geronimo, Hardin
DivergenceFree Multiwavelets
, 1998
"... . In this paper we construct IR n valued biorthogonal, compactly supported multiwavelet families such that one of the biorthogonal pairs consists of divergencefree vector wavelets. The construction is based largely on Lemari'e's idea of multiresolution analyses intertwined by different ..."
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by differentiation. We show that this technique extends nontrivially to multiwavelets via Strela's twoscale transform. An example based on the DonovanGeronimoHardinMassopust (DGHM) multiwavelets is given. x1. Introduction The study of divergencefree wavelets originated in the early 1990s with two
Multiwavelet Construction via the Lifting Scheme
 in Wavelet Analysis and Multiresolution Methods, T.X. He, ed., Lecture Notes in Pure and Appl. Math
, 1999
"... Lifting provides a simple method for constructing biorthogonal wavelet bases. We generalize lifting to the case of multiwavelets, and in so doing provide useful intuition about the additional degrees of freedom made available in the construction of multiwavelets. We show that any compactly suppo ..."
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Cited by 11 (0 self)
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supported multiwavelet transform can be decomposed into a sequence of lifting steps. Finally, we compare lifting to the twoscale similarity transform construction method. 1 Introduction The recent work of Geronimo et al [5] has generated considerable interest in multiwavelet constructions. In contrast
Preprocessing For Discrete Multiwavelet Transform Of TwoDimensional Signals
"... Multiwavelet transform can be implemented by treestructured matrix #lter bank, which operates on vector sequence input instead of scalar ones. Therefore, unlike in scalar wavelet system, preprocessing is usually required to extract vector sequence input from the input signal for better performance. ..."
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. A 2D approximationbased preprocessing scheme for GHM #Geronimo, Hardin and Massopust# discrete multiwavelet transform of 2D signals is proposed. Compared with the recent 1D approximationbased method, the proposed scheme reduces the preprocessing computational complexityby 65# while maintaining
The Discrete Multiple Wavelet Transform and Thresholding Methods
 IEEE Transactions in Signal Processing
, 1996
"... Orthogonal wavelet bases have recently been developed using multiple mother wavelet functions. Applying the discrete multiple wavelet transform requires the input data to be preprocessed to obtain a more economical decomposition. We discuss the properties of several preprocessing methods and their e ..."
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Cited by 37 (3 self)
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demonstrates that when using the Geronimo multiwavelet with an appropriate preprocessing method and bivariate thresholding, better results are obtained compared with using either univariate thresholding methods or thresholding Daubechies wavelets. 1 Introduction The development of wavelet theory has given
Application of symmetric orthogonal multiwavelets and prefilter technique for Image compression
 Journal of Computer Science and Technology
, 2003
"... Multiwavelets are new addition to the body of wavelet theory. There are many types of symmetric multiwavelets such as GeronimoHardinMassopust (GHM) and ChuiLian (CL) multiwavelets. However, the matrix filter generating the GHM system multiwavelets does not satisfy the symmetric property. For this ..."
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Cited by 2 (0 self)
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Multiwavelets are new addition to the body of wavelet theory. There are many types of symmetric multiwavelets such as GeronimoHardinMassopust (GHM) and ChuiLian (CL) multiwavelets. However, the matrix filter generating the GHM system multiwavelets does not satisfy the symmetric property
Balanced GHMLike Multiscaling Functions
, 1999
"... The Geronimo–Hardin–Massopust (GHM) multiwavelet basis exhibits symmetry, orthogonality, short support, and approximation order K = 2, which is not possible for wavelet bases based on a single scalingwavelet function pair. However, the filterbank associated with this basis does not inherit the zer ..."
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Cited by 6 (1 self)
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The Geronimo–Hardin–Massopust (GHM) multiwavelet basis exhibits symmetry, orthogonality, short support, and approximation order K = 2, which is not possible for wavelet bases based on a single scalingwavelet function pair. However, the filterbank associated with this basis does not inherit
Signal and Image Denoising via Wavelet Thresholding: Orthogonal and Biorthogonal, Scalar and Multiple Wavelet Transforms
 In Nonlinear and Nonstationary Signal Processing
, 1998
"... The method of signal denoising... In this paper we study wavelet thresholding in the context of scalar orthogonal, scalar biorthogonal, multiple orthogonal and multiple biorthogonal wavelet transforms. Two types of multiwavelet thresholding are considered: scalar and vector. Both of them take into a ..."
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Cited by 24 (2 self)
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functions). Section 3 introduces two classes of orthogonal multiwavelets which may be used in multifilter banks  the GeronimoHardinMassopust (GHM) and ChuiLian (CL) classes, while Section 4 discusses biorthogonal multifilter banks, denoted BiGHM and BiHermite. For multifilter banks the given scalar