As expected, in terms of signal denoising, the double-density complex wavelet transform performed much better at suppressing noise over the double-density wavelet transform. The new double-density dual-tree wavelet transform also outperformed the conventional separable wavelet transform, however, to improve the performance further it is necessary to use a different threshold for each subband because for this transform the wavelets associated with different subbands have different norms. We saw that the 2-D double-density method works best, followed by the double-density dual-tree complex wavelet transform, then the double-density dual-tree real wavelet transform (all of which outperform the standard 2-D DWT).

In terms of future research, the double-density dual-tree wavelet transform could be improved by instituting a subband-dependent threshold point. Because this transform has far more subbands than the double-density wavelet transform, it is expected that each subband possesses a different optimal threshold point. By altering the threshold per subband, it is expected that this transform may then outperform the double-density wavelet transform in terms of multi-dimensional denoising.

[1] I. W. Selesnick, "The Double Density DWT," in Wavelets in Signal and Image Analysis: From Theory to Practice, A. Petrosian and F. G. Meyer, Eds. Boston, MA: Kluwer, 2001.

[2] I. W. Selesnick, "The Double-Density Dual-Tree DWT," in IEEE Transactions on Signal Processing, 52(5): 1304-14, May 2004.

[3] I. W. Selesnick and A. F. Abdelnour, "Symmetric Wavelet Tight Frames With Two Generators," Applied and Computational Harmonic Analysis, to appear, 2004.