The Optimum Approximation of Multi-Dimensional Signals Using Parallel Wavelet Filter Banks

概要

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A systematic theory of the optimum sub-band interpolation using parallel wavelet filter banks is 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 L^2 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.
社団法人電子情報通信学会の論文
1993-10-25