Optimum interpolatory approximation in wavelet subspace

Takuro Kida; Yuichi Kida

doi:10.1117/12.366808

26 October 1999 Optimum interpolatory approximation in wavelet subspace

Takuro Kida, Yuichi Kida

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366808
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

In this paper, we will present a systematic discussion for the optimum interpolatory approximation in a shift-invariant wavelet and/or scaling subspace. Firstly, we will present the optimum interpolation functions which minimize various worst case measure of approximation error among all the linear and the nonlinear approximations using the same sample values of the input signal. Secondly, we will show that the optimum interpolation functions are expressed as the parallel shifts of the finite number of one function. Finally, we will present the optimum interpolation function in wavelet and scaling subspace. These interpolation functions are optimum in the multi-resolution analysis which considers lower resolutions.

Citation Download Citation

Takuro Kida and Yuichi Kida "Optimum interpolatory approximation in wavelet subspace", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366808

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