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Fractional B-splines | |
 The animation shows the fractional B-splines with an α that runs from 0 to 5. |
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| Note that these are valid scaling functions for all α >-1/2. | ||
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Symmetrized fractional B-splines | |
 The animation shows the symmetrized fractional B-splines with an α that runs from 0 to 5. |
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| Reference: M. Unser, T. Blu, "Fractional Splines and Wavelets," SIAM Review, vol. 42, no. 1, pp. 43-67, March 2000. |
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Fractional B-spline wavelets | |
 The animation shows the fractional B-spline wavelets with an α that runs from 0 to 5. |
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 QuickTime or MPEG |
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| Note that every single wavelet on this graph generates a stable wavelet basis of L2 (the space of finite energy functions). | ||
| References: M. Unser, T. Blu, "Fractional Splines and Wavelets," SIAM Review, vol. 42, no. 1, pp. 43-67, March 2000. M. Unser, T. Blu, "Construction of Fractional Spline Wavelet Bases," Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing VII, Denver CO, USA, July 19-23, 1999, vol. 3813, pp. 422-431. |
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