Now that we have successfully implemented all of the double-density and double-density dual-tree DWTs, we can use the transforms for noise attenuation in noisy signals and images.

In terms of one-dimensional applications, these new transforms will be used to denoise signals. This method is discussed in the section Signal Denoising. First we implement the double-density DWT denoising method, then the double-density complex DWT denoising method. Finally, we compare the two to determine which transform is best suited for noise attenuation in 1-D signals.

In the section Image Denoising, we introduce the application of the double-density, double-density dual-tree real, and double-density dual-tree complex DWTs for noise attenuation in photographic images.