Image Denoising Using Wavelets: Application in Medical Imaging - Advances in Heuristic Signal Processing and Applications - page 293

Fig. 13.11 Denoising of the
Lena image corrupted by
Gaussian white noise

• The soft thresholding function is continuous, but creates an attenuation on large

coefficients, which results in an oversmoothing and an important bias for the es-
timated signal;

• The NNG and SCAD functions achieve a certain compromise between the hard

and the soft thresholding functions.

However, all the standard Wavelet Shrinkage functions presented above include
zero-forcing. This zero-forcing induces singularities of the thresholding function.
As a consequence, it results in a significant variation of the estimation due to the sen-
sitivity of the inverse wavelet transform. In addition, thresholding rules assume that
the wavelet representation is sparse. Note that smooth signals yield sparse wavelet
representations in the sense given by: For such signals, large coefficients are very
few in number.
In contrast, wavelet representations of natural images, which tend to be piecewise
regular (where discontinuities are along smooth curves) rather than smooth, fail to
be sparse enough since large coefficients are not very few. This justifies the intro-
duction of more flexible wavelet shrinkage methods for correcting the drawbacks of
thresholding rules.
Figure 13.11 depicts the original Lena image (top left) and the same image made
artificially noisy (to the right) using Gaussian noise (randn function). This image has
been denoised (see Fig. 13.11 , bottom panel) using the Matlab function wdencmp
with a fixed soft threshold. The Matlab code for this application is as follows:

% Load Lena image and add Gaussian noise
load lena;
init = 2055615866; randn('seed',init);
x=X+15 * randn(size(X));
%Specification of fixed threshold and type of %thresholding
[thr,sorh,keepapp] = ddencmp('den','wv',x);
%Denoising using a symlet wavelet of order 4