23 October 1996 Theory and design of two-dimensional nonseparable shift-invariant filter banks
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Shift-variance limits the usage of 2D maximally-decimated filter banks in many image processing applications where shift-invariance is desired. Several approaches have been proposed to overcome this problem for both 1D and 2D multirate systems. All of the existing methods are 1D-based algorithms, i.e. dealing with 2D image by separable processing, and thus do not have the advantages that a non- separable 2D system offers. In this paper, a framework for the theory and the design of 2D shift-invariant filter banks with non-separable sampling and/or non-separable filters are presented. There are three major advantages that the proposed 2D shift-invariant filter banks have over the separable 2D systems using the existing methods. First of all, it is a non-separable 2D approach and therefore has the advantages that a 'true' 2D approach offers. Secondly, the resulting 2D filter banks and wavelets have the conventional dyadic structure while possessing better SI property. Finally, the proposed filter bank is independent of input images. Design examples are presented.
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Y. Hui, Y. Hui, C. W. Kok, C. W. Kok, Truong Q. Nguyen, Truong Q. Nguyen, } "Theory and design of two-dimensional nonseparable shift-invariant filter banks", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); doi: 10.1117/12.255240; https://doi.org/10.1117/12.255240

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