Title :
Quantitative L2 error analysis for interpolation methods and wavelet expansions
Author :
Blu, Thierry ; Unser, Michael
Author_Institution :
DSE/SGV, CNET, Issy-les-Moulineaux, France
Abstract :
Our goal in this paper is to set a theoretical basis for the comparison of re-sampling and interpolation methods. We consider the general problem of the approximation of an arbitrary continuously-defined function f(x)-not necessarily bandlimited-when we vary the sampling step T. We present an accurate L2 computation of the induced approximation error as a function of T for a general class of linear approximation operators including interpolation and other kinds of projectors. This new quantitative result provides exact expressions for the asymptotic development of the error as T→0, and also sharp (asymptotically exact) upper bounds
Keywords :
approximation theory; error analysis; image sampling; interpolation; wavelet transforms; arbitrary continuously-defined function; asymptotic development; image processing; induced approximation error; interpolation methods; linear approximation operators; projectors; quantitative L2 error analysis; re-sampling; sampling step; upper bounds; wavelet expansions; Approximation error; Error analysis; Fourier transforms; Image sampling; Interpolation; Linear approximation; Sampling methods; Space technology; Upper bound; Wavelet analysis;
Conference_Titel :
Image Processing, 1997. Proceedings., International Conference on
Conference_Location :
Santa Barbara, CA
Print_ISBN :
0-8186-8183-7
DOI :
10.1109/ICIP.1997.648000
