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Quantitative L2 Error Analysis for Interpolation Methods and Wavelet Expansions

T. Blu, M. Unser

Proceedings of the 1997 IEEE International Conference on Image Processing (ICIP'97), Santa Barbara CA, USA, October 26-29, 1997, vol. I, pp. 663-666.



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.


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