W-matrices, nonorthogonal multiresolution analysis, and finite signals of arbitrary length

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Wavelet theory and discrete wavelet transforms have had great impact on the field of signal and image processing. In this paper the authors propose a new class of discrete transforms. It ``includes`` the classical Haar and Daubechies transforms. These transforms treat the endpoints of a signal in a different manner from that of conventional techniques. This new approach allows the authors to efficiently handle signals of any length; thus, one is not restricted to work with signal or image sizes that are multiples of a power of 2. Their method does not lengthen the output signal and does not require ... continued below

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24 p.

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Kwong, M.K. & Tang, P.T.P. December 31, 1994.

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Wavelet theory and discrete wavelet transforms have had great impact on the field of signal and image processing. In this paper the authors propose a new class of discrete transforms. It ``includes`` the classical Haar and Daubechies transforms. These transforms treat the endpoints of a signal in a different manner from that of conventional techniques. This new approach allows the authors to efficiently handle signals of any length; thus, one is not restricted to work with signal or image sizes that are multiples of a power of 2. Their method does not lengthen the output signal and does not require an additional bookkeeping vector. An exciting result is the uncovering of a new and simple transform that performs very well for compression purposes. It has compact support of length 4, and so is its inverse. The coefficients are symmetrical, and the associated scaling function is fairly smooth The Associated dual wavelet has vanishing moments up to order 2. Numerical results comparing the performance of this transform with that of the Daubechies D{sub 4} transform are given. The multiresolution decomposition, however, is not orthogonal. They will see why this apparent defect is not a real problem in practice. Furthermore, they will give a method to compute an orthogonal compensation that gives them the best approximation possible with the given scaling space. The transform can be described completely within the context of matrix theory and linear algebra. Thus, even without prior knowledge of wavelet theory, one can easily grasp the concrete algorithm and apply it to specific problems within a very short time, without having to master complex functional analysis. At the end of the paper, they shall make the connection to wavelet theory.

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24 p.

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OSTI as DE95005846

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  • Gigabyte image processing workshop, Argonne, IL (United States), 8-9 Jul 1994

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  • Other: DE95005846
  • Report No.: ANL/MCS/CP--84114
  • Report No.: CONF-9407170--1
  • Grant Number: W-31109-ENG-38
  • Office of Scientific & Technical Information Report Number: 34399
  • Archival Resource Key: ark:/67531/metadc685016

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  • December 31, 1994

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  • July 25, 2015, 2:20 a.m.

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  • Dec. 16, 2015, 4:51 p.m.

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Kwong, M.K. & Tang, P.T.P. W-matrices, nonorthogonal multiresolution analysis, and finite signals of arbitrary length, article, December 31, 1994; Illinois. (digital.library.unt.edu/ark:/67531/metadc685016/: accessed September 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.