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SURE-LET for Orthonormal Wavelet-Domain Video Denoising Florian Luisier, Member, IEEE, Thierry Blu, Senior Member, IEEE, and Michael Unser, Fellow, IEEE IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 20, NO. 6, JUNE

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Outline Introduction SURE-LET principle – Stein’s Unbiased Risk Estimate (SURE) – Linear Expansion of Thresholds (LET) Algorithm – Global Motion Compensation – Local Motion Compensation by Selective Block-Matching – Multiframe Interscale Wavelet Thresholding – Computational Complexity Experiments Conclusion Result 2

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Introduction An efficient orthonormal wavelet-domain video denoising algorithm based on an integration of motion compensation into an adapted version SURE-LET approach. The results are even competitive with most state-of-the-art redundant wavelet-based techniques. 3

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SURE-LET principle This approach avoids any a priori hypotheses on the noise-free signal. 4

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Stein’s Unbiased Risk Estimate (SURE) SURE [18] is an unbiased statistical estimate of the mean squared error (MSE). 5

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Linear Expansion of Thresholds (LET) 6

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Algorithm 7

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Global Motion Compensation To increase the correlations between adjacent frames, we compensate for interframe motion using a global motion compensation 8

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Local Motion Compensation by Selective Block-Matching(1/5) The proposed selective block-matching procedure has two key advantages: – Fast – The interframe noise covariance matrix can be assumed to be unaffected by the local motion compensation contrary to standard block- matching 9

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Local Motion Compensation by Selective Block-Matching(2/5) parameters are therefore involved: 1) The size of the considered blocks: 8X16 2) The size of the search region: 15X15 3) The criterion used for measuring the similarity between blocks: MSE 4) The way of exploring the search region: Exhaustive search 10

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Local Motion Compensation by Selective Block-Matching(3/5) Perform motion compensation only in the blocks, where a significant motion between frames was detected. 11

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Local Motion Compensation by Selective Block-Matching(4/5) The block-matching itself is performed on the smoothed frames, in order to decrease the sensitivity to noise. 12

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Local Motion Compensation by Selective Block-Matching(5/5) The minimum of these MSEs (MSEmin) is considered as the “no motion level.” – Threshold λ2 MSEmin, where λ2 ≥ 1. Select λ1 = λ2 = 13

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Multiframe Interscale Wavelet Thresholding 14 we experimentally found that λ3 = λ2 = λ1 = gave the best result.

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Computational Complexity 15

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Experiments 16

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Experiments 17

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Experiments 18

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Conclusion Present a relatively simple and efficient video denoising algorithm. Favorably compare with most state-of-the-art redundant wavelet-based approaches, having a lighter computational load. Increase the shift-invariance of the proposed solution to reach the same level performance as the very best video denoising algorithm. 19

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Result / / 20

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