Image Denoising Using Wavelets: Application in Medical Imaging - Advances in Heuristic Signal Processing and Applications - page 290

Fig. 13.8 First level decomposition of the Contourlet Transform

true multiresolution and multidirectional image representation which can effectively
capture image edges and contour information in all directions; therefore, it is very
suited for image processing, namely in image denoising.
The Contourlet Transform is constructed by the Laplacian pyramid (LP) and di-
rectional filter banks (DFB) as illustrated in Fig. 13.8 . The LP decomposes images
into subbands and DFB analyzes each detail image.

13.3 Denoising or Noise Reduction

The challenge is to restore a useful signal when only a noisy version is available.
The idea consists simply in adequate modification of the coefficients (of the wavelet
transform of the observed signal) taking advantage of their local properties, then
inverting the transformation to obtain a noise-free version of the signal!
For a 1D signal, wavelet shrinkage denoising attempts to remove whatever noise
is present and retain whatever signal is present regardless of the frequency (or
scale) content of the signal. It is not a smoothing (averaging) of data. Smoothing
removes high frequencies and retains low frequencies. Consequently, for a 2D sig-
nal, smoothing introduces a blurring and loss of information.
Wavelet shrinkage denoising consists of three steps: a linear DWT, a nonlinear
shrinkage denoising, and a linear inverse DWT. This heuristic procedure is consid-