Image Denoising Using Wavelets: Application in Medical Imaging - Advances in Heuristic Signal Processing and Applications - page 289

Fig. 13.7 Example of decomposition (at three levels) into wavelet packets by cascading filtering
and decimation

13.2.3 Contourlet Transform

Do and Vetterli [ 12 ] have proposed the contourlet transform (CT), which is one
of several transforms developed in recent years, aimed at improving image mul-
tiresolution analysis based on discrete wavelet transform. The main feature of these
transforms is the potential to efficiently handle 2D singularities, i.e., edges, un-
like wavelets which can deal with point singularities exclusively. This difference
is caused by the two main properties that the CT possess:

•

Directionality, i.e., the representation should contain basis functions in many di-
rections, as opposed to only 3 directions (horizontal, vertical, and diagonal) of
wavelets,

• Anisotropy, i.e., the representation should capture smooth contours. It should con-

tain basis functions using a variety of elongated shapes with different aspect ra-
tios.

The main advantage of the CT over other geometrically-driven representations,
e.g., curvelets and bandelets, is its relatively simple and efficient wavelet-like im-
plementation using iterative filter banks. Consequently, the contourlet transform is a