Optimum interpolatory approximation in wavelet subspace
Takuro Kida, Yuichi Kida · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1999
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.