Combining the Power of Internal & External Denoising
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Combining the Power of Internal & External Denoising
Inbar MosseriThe Weizmann Institute of Science , ISRAELICCP , 2013
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Outline Introduction Background Patch_psnr Results
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Internal Denoising
NLM BM3D
Denoising using other noisy patches within the same noisy image
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External Denoising
EPLL Sparse
Denoising using external clean natural patches or a compact representation
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a) Original b) Noisy input c) Internal NLM d) External NLMe) Combinining (c)&(d)
Internal vs. External Denoising
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Internal vs. External Patch Preference
the higher the noise in the image, the stronger the preference for internal denoising
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var( )atchSNR(p ) var( )def
npPn
PatchSNR
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PatchSNRpatches with low PatchSNR (e.g., insmooth image regions) tend to prefer Internal denoising
patches with high PatchSNR (edges, texture) tend to prefer External denoising
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Overfitting the Noise-Mean
𝑝𝑛=𝑝+𝑛=�̂�+�̂��̂�=𝑝+𝑛�̂�=𝑛−𝑛
𝑅𝑀𝑆𝐸 𝑖𝑑𝑒𝑎𝑙=√𝐸𝑛 (𝑛2 )=√∫𝑛2𝑃𝑟(𝑛)𝑑𝑛=𝜎√𝑑
d : patch size ~ N(0, )
the empirical mean/variance of the noise within an individual small patch is usually not zero/σ2
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Fitting of the Noise Mean
The denoising error grows linearly with the deviation from zero of the empirical noise-mean within the patch. In contrast, the denoising error is independent of the empirical noise variance within the patch.
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For smooth patches with low var(p), after removing the mean , pn = p + n .
These patches are dominated by noise.There are high correlation between a random noise patch n and its similar natural patch NN(n)
Overfit the Noise Detail
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Overfit the Noise Detail
For smooth patches with low var(p), after removing the mean , pn = p + n .
These patches are dominated by noise.There are high correlation between a random noise patch n and its similar natural patch NN(n)
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Estimate the PatchSNR var( )var( )atchSNR(p ) 1var( ) var( )
nn
ppPn n
But var(n) is also unknown and patch-dependent.
we approximate var(n) using one of the existing denoising algorithm and get the denoised version of , so:
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