Image Denoising Using Wavelets: Application in Medical Imaging - Advances in Heuristic Signal Processing and Applications - page 292

Fig. 13.9 Hard thresholding
and soft thresholding

Donoho and Johnstone [ 13 ] have shown that the choice of S is near-optimal for

N 4.

Fig. 13.9 represents the thresholding procedure. Note that hard thresholding cre-
ates discontinuities at k

≥

1.
Heuristic denoising is based on the hard and soft thresholding functions (see
Fig. 13.9 ), the non-negative garrote (NNG) function and the smoothly clipped abso-
lute deviation (SCAD) function, both illustrated in Fig. 13.10 .
Although these standard thresholding functions are close to optimal, they raise
some limitations:

±

• The hard thresholding function is not everywhere continuous and its discontinu-

ities at k ± 1 generate a high variance in the estimated signal;

Fig. 13.10 NNG and SCAD shrinkage functions