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Multi-resolution analysis on the interval with natural spline projection and uniform two-scale relation

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Abstract

The aim of this paper is to present a modification to the Chui and Quak (1992) spline multiresolution analysis for the finite interval. Boundary scaling functions with multipole nodes at interval endpoints are rejected, in favor of the classical B-spline scaling function restricted to the interval. This necessitates derivation of revised boundary wavelets. In addition, a direct method of decomposition results in bandwidth reduction on solving some associated linear systems, and image distortion is reduced by employing natural spline projection. Finally, a hybrid projection scheme is proposed, which particularly for large systems further lowers operation count. Numerical experiments proving the algorithm are indicated.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Old Dominion University, 23529, Norfolk, Virginia

    Sang Kyu Yang & Charlie H. Cooke

Authors
  1. Sang Kyu Yang
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  2. Charlie H. Cooke
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Yang, S.K., Cooke, C.H. Multi-resolution analysis on the interval with natural spline projection and uniform two-scale relation. J Sci Comput 10, 391–407 (1995). https://doi.org/10.1007/BF02088957

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  • DOI: https://doi.org/10.1007/BF02088957

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