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Optimizing Basis Functions for Best Approximation

T. Blu, M. Unser, P. Thévenaz

Fifth International Conference on Curves and Surfaces (ICCS'02), Saint Malo, French Republic, June 27-July 3, 2002.



By evaluating approximation theoretic quantities we show how to compute explicitely the basis generators that minimize the approximation error for a full set of functions to approximate. We give several examples of this optimization, either to get the best generators that have maximal order for minimum support [1], or to design the best interpolation scheme with classical generators, such as B-splines [2]. We present practical examples that visually confirm the validity of our approach.

References

  1. T. Blu, P. Thévenaz, M. Unser, "MOMS: Maximal-Order Interpolation of Minimal Support," IEEE Transactions on Image Processing, vol. 10, no. 7, pp. 1069-1080, July 2001.

  2. T. Blu, P. Thévenaz, M. Unser, "Linear Interpolation Revitalized," submitted to IEEE Transactions on Image Processing.


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