BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

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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