September 12, 2008

A real duet - On dual-tree wavelets (and a Matlab toolbox)

True pieces of art elude science (left picture borrowed from Flickr). Anyway, dual-tree wavelets form a real duet in Hilbert transform type harmony. But the true deal comes from some software implementing this possibly complex wavelet decomposition.

Version 1.2 of the M-band dual-tree wavelet Matlab toolbox has been released. It is available from Caroline Chaux webpage or directly from the link:
http://www-syscom.univ-mlv.fr/~chaux/toolbox/TOOLBOX_DTMband1D_v1.2.zip

The toolbox implements several 2-band and M-band wavelets (e.g. Meyer 2, 3 and 4 bands, Haar, Shannon etc.) in the Hilbert transform based dual-tree wavelet framework. Theoretical results, applications and comparisons may be found in the following papers from
http://www-syscom.univ-mlv.fr/~chaux/publications.html

Image Analysis Using a Dual-Tree M-Band Wavelet Transform
IEEE Transactions on Image Processing, Vol. 15, No.8, Aug. 2006, p. 2397-2412

Noise Covariance Properties in Dual-Tree Wavelet Decompositions
IEEE Transactions on Information Theory, Vol. 53, No. 12, Dec. 2007, pp. 4680-4700.

A Nonlinear Stein Based Estimator for Multichannel Image Denoising
IEEE Transactions on Signal Processing, Vol. 56, No. 8, Aug. 2008, pp. 3855-3870.