Performs a nonredundant fractional wavelets transform of an image. The wavelet basis is specified within the family of fractional splines, which are the only wavelets to date that are tunable in a continuous fashion. Experiments this new family of wavelets with the plugin of the publicdomain software ImageJ. 
Installation: First, you have to get a copy of ImageJ at the download page of ImageJ web site. Next, you place the unzipped version of our software in the plugins folder of ImageJ. The whole process should not take more than a couple of minutes. ImageJ runs on several plateforms: Unix, Linux, Windows, Mac OS 9 and Mac OS X. 
Important note: You are free to use this software for research purposes, but you should not redistribute it without our consent. In addition, we expect you to include adequate citations and acknowledgments whenever you present or publish results that are based on it. 
References: M. Unser, T. Blu, "Fractional Splines and Wavelets," SIAM Review, vol. 42, no. 1, pp. 4367, March 2000. T. Blu, M. Unser, "The Fractional Spline Wavelet Transform: Definition and Implementation," Proceedings of the TwentyFifth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'00), Istanbul, Turkey, June 59, 2000, vol. I, pp. 512515. T. Blu, M. Unser, "A Complete Family of Scaling Functions: The (α, τ)Fractional Splines," Proceedings of the TwentyEighth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'03), Hong Kong SAR, People's Republic of China, April 610, 2003, in press. 
Authors: This plugin was implemented by Gil Gaillard, Daniel Sage, Dimitri Van De Ville and Emilio Casanova. 
Contact: daniel.sage@epfl.ch 
Open an image The Wavelet Transform plugin for ImageJ only works with images (no image sequences).

Functioning of the Wavelet Transform plugin

Step 1  Discrete Wavelet Transform: Analysis side The complete family of (bi)orthogonal spline wavelets with fractional degree (α) and arbitrary shift (τ) is available in this plugin
The scaling function or the wavelet are displayed in the central part of the plugin window. In this way, the user can visualize the effects of changing the transform parameters. When the image dimensions are not powers of two, an "Image size control" window allows you to crop or extend the original image dimensions. If the size is not a power of two, the algorithm still works but the processing will be very slow. Optionally  Processing You can use any ImageJ manipulations to process the wavelet coefficients Step 2  Inverse Discrete Wavelet Transform: Synthesis side The final step reconstructs the (processed) image or image sequence using the same settings as the analysis side 