Digital Signal Processing Reference
In-Depth Information
Figure 10.16. Denoising. (top) Simulated synchrotron image and same image with additive
Gaussian noise (i.e., simulated data). (middle) Undecimated wavelet filtering and residual.
(bottom) Pyramidal curvelet filtering and residual. (
See color plates.
)
10.7 RESTORATION AND DECOMPOSITION ON THE SPHERE
10.7.1 Denoising
Wavelets and curvelets have been used successfully for image denoising via non-
linear filtering or thresholding methods, as extensively studied in Chapter 6. In the
results of Fig. 10.16, denoising by hard thresholding the wavelet and curvelet co-
efficients on the sphere was used. The threshold was set to 4 times the standard
deviation of the noise at each subband.
Figure 10.16 describes the setting and the results of a simulated denoising ex-
periment: the original simulated map of the astrophysical synchrotron emission and
the same image plus additive Gaussian noise (
5). Because the synchrotron im-
age has a standard deviation (after renormalization) equal to 16
σ
=
.
26, the signal-to-
noise ratio (SNR) is around 3
25. The middle panels in this figure show the UWTS
denoised image and the residuals. The bottom panels show the pyramidal curvelet
.
