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Notes

The Daubechies D6 wavelet transform was used in all experiments. Results for the four images used in the paper plus two more (Barbara, Fingerprint) are shown.

Numerical results

1D Signals


Images


Visual Displays with sigma=20.0

Right-click and 'View Image' to see the full size version. 
$ ./mdldenoise data/lena.png 20    # noise sigma=20.0
none 20.026102 22.098875
visu 11.311243 27.060597
sure 8.553920 29.487500
bayes 8.188319 29.866908
rnml 14.501867 24.902325
inml 10.418491 27.774707
snml 9.250767 28.807248
mnml 8.669345 29.371078
Original Noisy (Rissanen, 2000)
MDL (A) MDL (A-B) MDL (A-B-C)
VisuShrink SureShrink BayesShrink 


$ ./mdldenoise data/boat.png 20    # noise sigma=20.0
none 19.997682 22.111210
visu 13.999332 25.208657
sure 10.237465 27.926955
bayes 9.754534 28.346673
rnml 15.786528 24.165071
inml 13.061061 25.811235
snml 11.576499 26.859259
mnml 10.798660 27.463406
Original Noisy (Rissanen, 2000)
MDL (A) MDL (A-B) MDL (A-B-C)
VisuShrink SureShrink BayesShrink 


$ ./mdldenoise data/house.png 20    # noise sigma=20.0
none 20.048595 22.089125
visu 11.781003 26.707159
sure 9.267566 28.791490
bayes 8.799919 29.241230
rnml 14.916156 24.657665
inml 10.981392 27.317656
snml 9.863250 28.250403
mnml 9.246546 28.811213
Original Noisy (Rissanen, 2000)
MDL (A) MDL (A-B) MDL (A-B-C)
VisuShrink SureShrink BayesShrink 


$ ./mdldenoise data/peppers256.png 20    # noise sigma=20.0
none 20.047112 22.089767
visu 14.117754 25.135491
sure 11.272952 27.090051
bayes 10.306547 27.868540
rnml 14.925664 24.652130
inml 13.013526 25.842904
snml 11.476195 26.934846
mnml 10.660714 27.575078
Original Noisy
PSNR=22.1		 (Rissanen, 2000)
PSNR=24.7
MDL (A)
PSNR=25.8		 MDL (A-B)
PSNR=26.9		 MDL (A-B-C)
PSNR=27.6
VisuShrink
PSNR=25.1		 SureShrink
PSNR=27.1		 BayesShrink
PSNR=27.9		 


$ ./mdldenoise data/barbara.png 20    # noise sigma=20.0
none 20.040372 22.092688
visu 17.357708 23.340956
sure 11.801229 26.692259
bayes 11.596962 26.843919
rnml 15.605541 24.265227
inml 16.352231 23.859263
snml 14.467264 24.923075
mnml 13.301898 25.652531
Original Noisy (Rissanen, 2000)
MDL (A) MDL (A-B) MDL (A-B-C)
VisuShrink SureShrink BayesShrink 


$ ./mdldenoise data/fingerprint.png 20    # noise sigma=20.0
none 20.036335 22.094438
visu 19.321036 22.410195
sure 12.613739 26.113927
bayes 11.413956 26.982080
rnml 16.925600 23.559922
inml 17.465751 23.287058
snml 12.228512 26.383331
mnml 12.144918 26.442912
Original Noisy (Rissanen, 2000)
MDL (A) MDL (A-B) MDL (A-B-C)
VisuShrink SureShrink BayesShrink