Harold Christopher Burger , Stefan Harmeling

Improving Denoising Algorithms via a Multi-scale Meta-procedure
1
2
Harold Christopher Burger , Stefan Harmeling
Teaser: Results on strong noise
[email protected]; [email protected]
Approach outline
Results of our approach vs. Estrada’s [3]
for six denoising algorithms [2], [4], [6], [5], [1]
KSVD
FoE
4
4
3
3
1
12
0
−1
−2
−3
baseline KSVD
MS−KSVD (our approach)
Estrada−KSVD
−5
BM3D [1]
BM3D+our approach
PSNR: 18.88dB
PSNR: 20.96dB
12
2
10
1
3
0
−1
−2
−3
−4
−4
noisy, σ = 200
PSNR: 7.59dB
3
1
PSNR diff to FoE [dB]
PSNR diff to KSVD [dB]
2
BRFoE
PSNR diff to BRFoE [dB]
1
−6
0
50
100
150
Stddev of the noise (σ)
6
4
4
3
2
1
2
0
−2
baseline FoE
MS−FoE (our approach)
Estrada−FoE
−5
−6
0
200
8
50
100
Stddev of the noise (σ)
Wiener
baseline BRFoE
MS−BRFoE (our approach)
Estrada−BRFoE
−4
−6
0
150
50
100
150
Stddev of the noise (σ)
Bilateral Filtering
10
2
200
BM3D
3
4
Denoising by downscaling
4
23
0
baseline Wiener
MS−Wiener (our approach)
Estrada−Wiener
−5
0
→
7.61 dB
↓
↓
11
12
11
10
9
8
0
50
100
150
200
250
downsampled clean
downsampled noisy
10
9
8
7
6
5
clean
noisy
14
13
12
11
10
9
8
0
10
20
30
7
0
50
100
150
200
250
noisy
down-sampled
up-sampled
→ Down-scaling averages out the uncorrelated values of
the noise.
Recovering low frequencies
Shrinking high frequency coefficients
3
1
0
−1
−2
−3
1
2
3
0
−1
−2
−3
−4
−4
−5
0
baseline Bilateral Filtering
MS−Bilateral Filtering (our approach)
Estrada−Bilateral Filtering
50
100
150
Stddev of the noise (σ)
200
baseline BM3D
MS−BM3D (our approach)
Estrada−BM3D
−5
−6
0
50
100
150
Stddev of the noise (σ)
200
Results compared to BM3D [1]
MS−BM3D (our approach)
MS−KSVD (our approach)
BLS−GSM
2
1
0
BM3D
−1
−2
0
plain KSVD (baseline)
MS−KSVD, no thresholding
MS−KSVD, with thresholding
2.5
K−SVD
50
100
150
Stddev of the noise (σ)
200
2
1.5
References
1
[1] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian. Image denoising by sparse 3-D transformdomain collaborative filtering. IEEE Transactions on Image Processing, 16(8):2080–2095, 2007.
0.5
0
−0.5
→ Denoising algorithms are not good at recovering large
scale (low frequency) information.
200
2
4
KSVD
Improvement over plain KSVD [dB]
log power spectral density
13
15
log power spectral density
clean
noisy
14
log power spectral density
15
7
20.17 dB
↓
PSNR diff to BM3D [dB]
→
Why it works:
• Images have most energy in low frequencies.
• Noise is uniformly spread across the spectrum.
• Many denoising algorithms are not good at recovering low
frequency information.
• Down-sampling effectively transforms low-frequency information into high-frequency information.
50
100
150
Stddev of the noise (σ)
2
1
PSNR diff to BM3D [dB]
1. Denoise at different scales
2. Combine results using Laplacian pyramids.
5
PSNR diff to Bilateral Filtering [dB]
PSNR diff to Wiener [dB]
3
0
50
100
150
Stddev of the noise (σ)
200
true
denoised thresholded
thresholding helps
→ At very high noise levels, the denoising algorithm becomes incompetent at recovering high-frequencies.
[2] M. Elad and M. Aharon. Image denoising via sparse and redundant representations over learned
dictionaries. IEEE Transactions on Image Processing, 15(12):3736–3745, 2006.
[3] F. Estrada, D. Fleet, and A. Jepson. Stochastic image denoising. In Proc. BMVC, 2009.
[4] S. Roth and M.J. Black. Fields of experts. International Journal of Computer Vision, 82(2):205–
229, 2009.
[5] C. Tomasi and R. Manduchi. Bilateral filtering for gray and color images. In Proceedings of the
Sixth International Conference on Computer Vision, pages 839–846, 1998.
[6] Y. Weiss and W.T. Freeman. What makes a good model of natural images? In Proceedings of the
IEEE Conference on Computer Vision and Pattern Recognition, pages 1–8, 2007.