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The Optimum Approximation of Muliti-Dimensional Signals Using Parallel Wavelet Filter Banks
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1993/10/25
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Parallel/Multidimensional Signal Processing
multi-dimensional signals, optimum approximation, wavelet filter bank,
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A systematic theory of the optimum sub-band interpolation using parallel wavelet filter banks presented with respect to a family of n-dimensional signals which are not necessarily band-limited. It is assumed that the Fourier spectrums of these signals have weighted L2 norms smaller than a given positive number. In this paper, we establish a theory that the presented optimum interpolation functions satisfy the generalized discrete orthogonality and minimize the wide variety of measures of error simultaneously. In the following discussion, we assume initially that the corresponding approximation formula uses the infinite number of interpolation functions having limited supports and functional forms different from each other. However, it should be noted that the resultant optimum interpolation functions can be realized as the parallel shift of the finite number of space-limited functions. Some remarks to the problem of distinction of images is presented relating to the generalized discrete orthogonality and the reciprocal property for the proposed approximation.