Quantitative $ L ^{ 2 } $ Error Analysis for Interpolation Methods and Wavelet Expansions

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 $ L ^{ 2 } $ 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.


Published in:
Proceedings of the 1997 IEEE International Conference on Image Processing (ICIP'97), Santa Barbara CA, USA, 663–666
Year:
1997
Publisher:
IEEE
Laboratories:




 Record created 2015-09-18, last modified 2018-03-17

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