'A trous' Wavelet Filter

Authors: Olivier Marchal (marchal_olivier at hotmail.fr)
and Jerome Mutterer (jerome.mutterer at ibmp-ulp.u-strasbg.fr)
History: 2005/02/14: First version
2009/10/13: Emil Martinec fixed a bug in convolution between the image and a 2D B3-spline function
Limitations:Only works with 8-bit images
Source: A_trous_wavelet_filter.java
Installation: Download A_trous_wavelet_filter.java to the plugins folder and compile it with the "Compile and Run" command.
Restart ImageJ to add the "A trous filter" command to the Plugins menu.
Description: This plugin's purpose is to remove noise from noisy images. It makes use of image reconstruction from thresholded 'A trous' wavelet transform coefficients. Thresholding factors should be input in the dialog, and will influence the amount of noise removed. An image with the removed noise can be generated.

Finding adequate factors is critical to remove sufficient noise without affecting signal, and these factors may vary from one image type to another. A major advantage of the 'a trous' transform often used in multiscale analysis over e.g. the Haar transform is to avoid introduction of blocks artifacts.


References :
  • Holschneider, M., Kronland-Martinet, R., Morlet, J., and Tchamitchian, Ph., 1989. A real-time algorithm for signal analysis with the help of the wavelet transform. In J.M. Combes, A. Grossman and Ph. Tchamitchian, Eds., Wavelets: Time-Frequency Methods and Phase Space (Berlin: Springer-Verlag), pp. 286-297.
  • Shensa, M.J., 1992. Discrete Wavelet Transforms: Wedding the a trous and Mallat algorithms. IEEE Transactions on Signal Processing, 40, pp. 2,464-2,482.
  • Starck, J.-L., Murtagh, F., and Bijaoui, A., 1998. Image Processing and Data Analysis: The Multiscale Approach (Cambridge: Cambridge University Press).
  • 'A trous' algorithm adapted from Image Processing and Pattern Recognition by Jon Campbell and Fionn Murtagh.
  • Noise removal algorithm adapted from Multiscale Analysis Methods in Astronomy and Engineering by Jean Luc Starck and Fionn Murtagh.
This filter is macro-recordable, see the Haar wavelet filter for details.

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