Simulation with the classical Lena image
Original image and noisy image (sigma=20)
Orthogonal WT (7-9 filters) + univeral thresholding and residual image
Undecimated WT (7-9 filters) + ksigma thresholding and residual image
Wavelet-domain Hidden Markov Models and residual image
Multiscale entropy and residual image
Ridgelet transform and residual image
Curvelet transform and residual image
Combined filtering and residual image
Zoom on a part of the image
Color image filtering
Table 1:
PSNR after filtering the simulated image (Lena + Gaussian noise (sigma=20)).
| Method |
PSNR |
Comments |
|
|
|
| Noisy image |
22.13 |
|
|
|
|
| FWT7-9 + Universal Hard thresh. |
28.35 |
many artifacts |
|
|
|
| UWT7-9 + ksigma Hard thresh. |
31.94 |
very few artifact |
|
|
|
| UWT7-9 + Multiscale entropy |
32.10 |
no artifact |
|
|
|
| WHMM |
30.80 |
some noise remains |
|
|
|
| Ridgelet (B=8) |
29.99 |
artifacts |
|
|
|
| Ridgelet (B=16) |
30.87 |
few artefacts |
|
|
|
| Ridgelet (B=32) |
30.97 |
few artefacts |
|
|
|
| Ridgelet (B=64) |
30.79 |
few artefacts |
|
|
|
| Curvelet (B=16) |
31.95 |
no artifact |
|
|
|
| Combined filtering |
32.72 |
no artifact |
|
|
|
|
From this simulation, we can conclude that:
- The curvelet transform do a better job than the ridgelet transform,
whatever the block size.
- Undecimated wavelet transform produces comparable PSNR than the
curvelet transform (a little bit better for the multiscale entropy),
but the curvelet filtered image has a better visual quality.
- Only a combination of methods allows us to clean properly the residual.