Shape-Adaptive Transforms Filtering


Pointwise Shape-Adaptive DCT Denoising


Pointwise Shape-Adaptive DCT
EXPERIMENT RESULTS



All the results (images and tables) presented in this page have been obtained with our algorithms based on the low-complexity SA-DCT and can be replicated using the Pointwise Shape-Adaptive DCT Demobox.

For completeness, we also provide on a separate page some results which have been obtained by replacing the SA-DCT with the more complex “Shape-Adapted” DCT (obtained by orthogonalization of a set of DCT basis functions).


Denoising

Color denoising

Deblocking

Deblurring

noisy filtering denoised
noisy filtering denoised
JPEG filtering deblocked
blurred filtering deblurred



Denoising


Pointwise SA-DCT denoising
Results (PSNR, dB), noise is white additive Gaussian with variance σ².
(Click on the numbers to see the corresponding images)
σLena
512x512
Boats
512x512
House
256x256
Peppers
256x256
Cameraman
256x256
Barbara
512x512
Hill
512x512
Lake
512x512
5 38.54 37.14 39.38 37.99 38.15 37.47 37.03 36.61
10 35.58 33.63 35.98 34.46 33.98 33.48 33.43 32.81
15 33.86 31.79 34.14 32.44 31.70 31.37 31.60 30.98
20 32.62 30.49 32.92 31.04 30.19 29.99 30.39 29.74
25 31.66 29.47 31.92 29.92 29.10 28.94 29.50 28.79
30 30.85 28.64 31.10 29.02 28.24 28.09 28.80 28.01
35 30.17 27.93 30.39 28.26 27.52 27.35 28.22 27.35
50 28.60 26.26 28.67 26.55 25.89 25.44 26.85 25.83
75 26.76 24.62 26.58 24.57 23.89 23.51 25.44 24.14
100 25.50 23.52 25.07 23.15 22.49 22.49 24.47 22.96





Color Denoising


Pointwise SA-DCT denoising with structural constraint in luminance-chrominance space
Results (PSNR, dB), noise is white additive Gaussian with variance σ² on all RGB channels.
(Click on the numbers to see the corresponding images)
σLena
512x512
Peppers
512x512
Baboon
512x512
House
256x256
Lake
512x512
F-16
512x512
1034.9533.7030.6235.6732.3436.41
1533.5832.4228.3334.0930.5234.67
2032.6131.5726.8932.9729.4033.41
2531.8530.9025.8632.1228.5832.42
3031.2130.3325.0731.3927.9331.59
3530.6529.8124.4430.7427.3830.88
5029.2728.5323.0329.1326.1029.19
7527.7727.0721.4627.3924.6827.43




Deblocking


Pointwise SA-DCT deblocking and deringing for JPEG-compressed color images.
Results (PSNR, dB)
(Click on the numbers to see the corresponding images)
Quality
Q
LenaPeppersBaboonF-16HouseLakeTiffany
JPEG (bpp)SA-DCTJPEG (bpp)SA-DCTJPEG (bpp)SA-DCTJPEG (bpp)SA-DCTJPEG (bpp)SA-DCTJPEG (bpp)SA-DCTJPEG (bpp)SA-DCT
4 23.34 (0.12)24.79 22.32 (0.13)23.77 19.28 (0.17)20.00 23.68 (0.13)25.07 22.63 (0.15)23.76 21.16 (0.15)22.36 23.48 (0.10)24.56
6 25.52 (0.16)27.09 23.99 (0.17)25.54 20.38 (0.26)21.05 25.05 (0.17)26.43 24.41 (0.19)25.66 22.73 (0.21)23.84 25.17 (0.12)26.23
8 26.64 (0.19)28.16 24.99 (0.21)26.40 21.12 (0.35)21.71 26.15 (0.22)27.57 25.16 (0.24)26.41 23.75 (0.27)24.78 26.23 (0.15)27.18
10 27.53 (0.23)29.06 25.77 (0.25)27.11 21.63 (0.43)22.13 26.87 (0.25)28.30 26.25 (0.27)27.54 24.39 (0.32) 25.34 26.83 (0.19)27.76
15 28.97 (0.31)30.33 26.88 (0.33)27.99 22.49 (0.62)22.88 28.09 (0.34)29.45 27.52 (0.34)28.66 25.44 (0.44)26.27 27.89 (0.26)28.58
20 29.83 (0.38)31.00 27.57 (0.40)28.53 23.07 (0.77)23.37 28.90 (0.42)30.13 27.87 (0.41)28.75 26.07 (0.55)26.79 28.40 (0.32)28.99
25 30.44 (0.44)31.46 28.04 (0.47)28.90 23.50 (0.92)23.75 29.58 (0.48)30.71 28.55 (0.47)29.44 26.51 (0.64)27.13 28.91 (0.39)29.40
30 30.91 (0.50)31.79 28.40 (0.54)29.14 23.85 (1.05)24.06 30.06 (0.55)31.09 28.96 (0.54)29.76 26.84 (0.73)27.38 29.21 (0.45)29.62
40 31.54 (0.61)32.26 28.83 (0.66)29.45 24.40 (1.29)24.56 30.64 (0.66)31.52 29.51 (0.65)30.20 27.31 (0.88)27.78 29.57 (0.56)29.87
50 32.02 (0.72)32.63 29.25 (0.78)29.81 24.85 (1.51)24.97 31.06 (0.76)31.83 29.80 (0.76)30.40 27.66 (1.03)28.07 29.91 (0.67)30.12
75 33.21 (1.13)33.56 30.29 (1.23)30.67 26.21 (2.33)26.25 32.61 (1.16)33.18 31.44 (1.18)32.00 28.65 (1.58)28.91 31.03 (1.10)31.19
95 35.88 (3.19)35.88 32.07 (3.65)32.14 28.85 (5.55)28.66 34.92 (2.97)35.07 33.11 (0.76)33.20 30.88 (4.32)30.84 32.42 (3.14)32.33




Deblurring


Pointwise SA-DCT regularized deconvolution
Results for four different deblurring experiments (see below)
(Click on the numbers to see the corresponding images)
Experiment #1234
ISNR (dB)8.578.256.344.52

Experiment 1 - Cameraman 256x256, blur: 9x9 uniform "box-car" blur, Gaussian white noise: BSNR 40dB (σ²=0.308)
Experiment 2 - Cameraman 256x256, blur: 15x15 1/(x²+y²), x,y=-7,...,7, kernel, Gaussian white noise: σ²=2
Experiment 3 - Cameraman 256x256, blur: 15x15 1/(x²+y²), x,y=-7,...,7, kernel, Gaussian white noise: σ²=8
Experiment 4 - Lena 512x512, blur: 5x5 separable [1, 4, 6, 4, 1]/16 filter, Gaussian white noise: σ²=49









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