Thresholding Operators for Denoising

As a general rule, wavelet coefficients with larger magnitude are correlated with salient features in the image data. In that context, denoising can be achieved by applying a thresholding operator to the wavelet coefficients (in the transform

Figure 6.9: A Multiscale framework of denoising and enhancement using discrete dyadic wavelet transform. A three-level decomposition was shown.

domain) followed by reconstruction of the signal to the original image (spatial) domain.

Typical threshold operators for denoising include hard thresholding:

0, if |x| < T soft thresholding (wavelet shrinkage) [33]:

x —

T,

if

x > T

PT(x) =

x +

T,

if

x < — T,

0,

if

and affine (firm) thresholding [34]:

PT (x) =

x,

if

|x| > T

2x + T,

if

— T < x < —T/2

2x — T,

if

T/2 < x < T

0,

if

The shapes of these thresholding operators are illustrated in Fig. 6.10.

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