76740142基于噪声注入强大的噪声估计.pdf

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1、RobustRobust NoiseNoise EstimationEstimationBasedBased onon NoiseNoise InjectionInjectionChongwu Tang, Xiaokang Yang, and Guangtao ZhaiShanghai Key Labs of Digital Media Processing and Communication,Shanghai Jiao Tong University, Shanghai, Chinatangcw,xkyang,Abstract.Abstract. Noise estimation is an

2、 important premise for image denois-ing and the related research therefore has drawn increasing attentionand interest. Recent studies show that the distribution mode of localvariances in natural image can be used as a simple yet efficacious esti-mator of the additive noise variance, no matter what d

3、istribution thenoise follows. However, this type of method has the limitation that thetarget image must have a sufficiently large area with low pixel valuevariations. Furthermore, this type of noise estimator almost always leadto overestimation without taking into account the mode of local vari-ance

4、 distribution of the noise-free image in textural regions. To im-prove the accuracy of distribution-mode analysis type of noise estimationand to resolve the problem of overestimation, we propose a novel algo-rithm using a cascade of waveletsub-band estimation and noise-injectionbased rectification.

5、The proposed algorithm reduces the detrimental in-fluence of textural image area, and therefore alleviating overestimation ofthe noise variance. Extensive experiments and comparative study showthe reliability and superiority the proposed method over some existingcompetitors.Keywords:Keywords: noise

6、estimation, mode, wavelet transform, noise injection.1 1IntroductionIntroduction andand RelatedRelated WorksWorksNoise reduction is an essential step for many image processing and patternrecognition tasks. Most of existing denoisers depend on prior knowledge of noise.Studies show that performance of

7、 state-of-the-art image denoising algorithmscan drop dramatically given the wrong estimate of noise variation. As an conse-quence, an effective noise estimation method is of both theoretical and practicalimportance to nowadays image processing/analysis algorithms and systems.Since noise estimation f

8、rom a degraded image should be a blind process, theonly prior information of the noise we can assume is the distribution type, suchas additive White Gaussian Noise. Early attempts of image noise estimation dateback to Gonzalez, who proposed a noise estimation method based on noisy pixelsampling from

9、 smooth regions of the noise-free image 1. This pioneering methodis simple but clearly of low accuracy. Later some more sophisticated statisticalW. Lin et al. (Eds.): PCM 2012, LNCS 7674, pp. 142152, 2012.c Springer-Verlag Berlin Heidelberg 2012Robust Noise Estimation Based on Noise Injection143type

10、 of algorithms were proposed, which can be classified into spatial domainalgorithms and transform domain algorithms. The spatial domain algorithmsare mostly based on the statistics of image local variances, which usually involvethe following steps: First, suppress the original image contents to prev

11、ent over-estimation 2; Second, extract the mask of edges from the suppressed image tofurther reduce the influence of the original image structure; Third, calculate localvariances of the remaining content and use histogram statistics method to gen-erate an estimation of noise variance. Beyond these b

12、asic steps, some variationsand improvements were also proposed. In 2, Rank et al. first used a cascade oftwo 1-D difference operators to filter the noisy image, then computed the his-togram of local variances by dividing the remained image into some sub-regions,and the noise variance can be estimate

13、d by averaging the weighted histogram. In3,4,5, Laplacian filtering and Sobel edge extraction were used to get the edgemask. Block based local variances were calculated and the maximum or meanof the variances was taken as the estimator. Amer and Dubois further proposeda structure-oriented method to

14、enhance the robustness of noise estimation forimages with large texture areas 6. In 7, noise level was estimated from the gra-dients of smooth or small texture regions for each intensity interval. Despite ofthe low computational complexity,those spatial domain methods usually cannotavoid the influen

15、ce of original image structures and therefore have low accuracy.Moreover, image texture and structure cannot be satisfactorily detected underhigh noise level.Transform domain noise estimation algorithms were proposed along with thedevelopment of multi-resolution analysis and wavelet theory. Since th

16、e high-frequency wavelet sub-band contains a great part of noise information, and theunitary wavelettransform basis will not alter the statistical property of the noisein sub-bands, Donoho et al. proposed in 9 a robust noise level estimator whichis the median absolute value of wavelet coefficients a

17、t the highest resolution:median(|y(i)|), y(i) HHi(1)0.6745Though being widely used, the estimator in Eq. (1) tends to overestimate thenoise variance when the SNR in the wavelet components is high. In 8, Stefanoet al. proposed nonlinear statistical noise estimation functions and designed a setof trai

18、ning based in wavelet domain. Zlokolica et al. proposed a wavelet basedmethod for spatial-temporal noise estimation by analyzing the distributions ofspatial and temporal gradients which were determined from the finest scale ofthe spatial and temporal wavelet transform 10. Recently, Liu et al. propos

19、eda framework for automatic color noise estimation from a single image usingpiecewise smooth image models 11. A novel continuous function describingthe relationship between noise level and image brightness was proposed and anupper bound of the noise level was estimated by fitting a lower envelope to

20、 thestandard deviations of per-segment image variances. These algorithms havegoodperformance at the expense of higher computation complexity. n=144C. Tang, X. Yang, and G. ZhaiAnother widely used noise estimation method is matching moment 12. The2nd and 4th moments of the noisy image are used for no

21、ise variance estimation.This method performs well in low level noise conditions, but tends to under-estimate for lower noise level. All the aforementioned exiting algorithms havetheir own limitations of low estimation accuracy or high computational com-plexity.Towardsa fast and reliable estimator fo

22、r additive noise, Fern andez et al.presented a novel approach based on distribution of local sample statistics 13.The mode of the local variance distribution can be used as a fairly good estima-tor of the variance of additive noise, despite of noises distribution. Accordingto their works, the image

23、to deal with must has a sufficiently great proportionof low-variability areas so as to validate the local hypothesis of “constant plusnoise”, i.e. the mode of the local variance distribution is approximately zero.When additive noise is injected, the mode is right shifted for an amount cor-responding

24、 to noise variance. This “constant plus noise” assumption, thoughturned out to be valid for many real world images, may not hold well for im-ages with plenty of textures. Furthermore, the estimator almost always lead tooverestimation because the mode of local variance of the noise-free image isnot t

25、aken into account. For textural images, the extent of overestimation willbe even larger. To solve this problem, Lukin et al. adopted a pre-segmentationstep to extract the homogeneous areas of the textural image, and the mode oflocal variance of these areas can improve the estimation accuracy conside

26、rably14. However, the unsupervised variational classification method they adoptedin 14 had a high computation complexity that is not suitable for real-timeapplications.Since the level of noise varies from one iteration to another in the recursivefiltering scheme in some image restoration algorithms,

27、 it is always beneficial tohavean effective and robust noise estimation algorithm. In this paper, we presenta wavelet sub-band and noise injection based two-step scheme to estimate thevariance of additive noise. The first step is to suppress the impact of noise-freeimage structures, in which we extr

28、act the high frequency waveletsub-band of theimage and then apply the mode estimator to get a preliminary estimation of noisevariance. Second, we introduce a rectify procedure to tackle with the problem ofoverestimation. A test noise of known variance is injected into the original noisyimage to prod

29、uce a test “noisy image” that will undergo the same estimationprocedure in the first step and generate a rectify value, which will then be usedto improve the preliminary estimation. This rectify step effectively alleviates theoverestimation, especially for the textural images. Extensive comparative

30、studyshow the superiority and robustness of our proposed algorithm compared withit in 13.The rest of the paper is organized as follows. In Section 2, we analyze the noiseestimation problem and then introduce the wavelettransform and noise injectionbased estimation algorithm. Experiments and comparis

31、ons are presented anddiscussed in Section 3. Finally, concluding remarks are given in Section 4.Robust Noise Estimation Based on Noise Injection1452 22.12.1WaveletWavelet TransformTransform andand NoiseNoise InjectionInjection BasedBased NoiseNoiseEstimationEstimationTheThe LocalLocal VarianceVarian

32、ce DistributionDistribution andand ModeMode EstimatorEstimatorConsider an additive noise modely = x + n(2)where y, x, n represent the noisy image, original image and noise signal, respec-tively. Note that the original image and noise are always independent, the localvariance of noisy image can be wr

33、itten as222= x+ nylocloc(3)22let yand xbe local variance of noisy image and original image. Accordingloclocto the hypothesis in 13, the local areas should have relatively low variance2for many natural images, i.e. the distribution of xhas a very large peakloc2and a mode close to zero. Consequently,

34、the mode of yloccan be a reasonable2estimator towards noise variance n. Figure 1 illustrates the mode estimationof noise variance, from which we can see the local variance distribution of noisyimage are just right-shift versions of original images, and the shift amount is2, approximately.equal to nF

35、ig.Fig. 1.1. Mode estimation of noise variance.(a) is the original image Lena, (b) is the noisy2= 400. Sub-figures in the bottom row are the distributionsimage with 0 mean and nof their local variances, respectively. The local variances are sampled by a point-wisemanner, using a 7 7 window. For easy

36、 to see, the distributions are normalized to0,1.146C. Tang, X. Yang, and G. ZhaiHowever, the hypothesis mentioned above is found to be fallible in some situ-ations. Textural images such as fingerprint image and some natural images withcomplex scenes are not kurtotic enough near their local variances

37、. Figure 2 givessome examples of these images, and the distribution of their local variances areshown in the top row of Figure 3. The texture-rich property of these imagesmakes the modes of their local variance distribution far from zero and evenmulti-modal. The local variances are sampled using win

38、dows of different sizes.Larger sample window tends to contain more textural parts of the images, thedistribution of larger sample window are less kurtotic as it shows in non-texturalimages. Moreover, though the mode of original images local variance distribu-tion is minor, it will still lead to over

39、estimation if used straightforwardly.In 13,Fern andez et al. gavea rectification step of mode estimator through investigatingstatistical model of sample variance:2= nN 12modeylocN 3(4)where N is the number of samples. If N is too large, the rectification can beneglected.Fig.Fig. 2.2. Textural images

40、. From left to right: FINGERPRINT; CANYON; RAFTING;RACING.Based on the analysis above, we propose a novel algorithm which integratetexture suppression and noise injection based rectification to tackle with theaforementioned problems of mode estimator in subsection 2.2 and 2.3.2.22.2PreliminaryPrelim

41、inary Estimation:Estimation: ModeMode EstimatorEstimator inin High-FrequencyHigh-FrequencyWaveletWavelet Sub-bandSub-bandIn this subsection, we introduce the preliminary estimation step based on wavelettransform. The high-frequency (HF) wavelet sub-band of the noisy image con-tains majority of the n

42、oise information while abandoning most original imagestructures. As a result, the local variance of the HF sub-band will be low anddistributes around the value of noise variance, i.e. the mode estimator in HFsub-band will be a better indicator of the noise variance compared with the re-sult calculat

43、ed straightforwardly from the local variance distribution of originalnoisy image. Figure 3 is the comparisons of local variance distribution from orig-inal images (as illustrated in Figure 1) and their HF wavelet sub-bands, whereRobust Noise Estimation Based on Noise Injection147Fig.Fig. 3.3. Compar

44、isons of local variances normalized PDF between original images andtheir HF sub-bands. Top row: local variances distribution of original images. Bottomrow: local variances distribution of CD sub-bands. Sampled by point-wise manner,using 3 3, 7 7, 11 11, 31 31 windows.we can find that for textural im

45、ages, the local variance of HF sub-band obeysthe hypothesis better, no matter which size of window used for sampling.Consequently, We apply 1-level wavelet transform on the noisy image to getthe HF sub-band. The horizontal detail sub-band CH and vertical detail sub-band CV are found to be sensitive

46、to directional edges and are not ideal fornoise estimation. Therefore the diagonal detail sub-band CD should be chosenas the optimal HF substitute of the original noisy image. In our application, db1wavelet basis is used because it is unitary so as to preserve the noise variancein the transform doma

47、in. Then preliminary estimation of noise variance can becalculated on CD sub-band using Eq. (4).2.32.3AdvancedAdvanced Estimation:Estimation: NoiseNoise InjectionInjection BasedBased RectificationRectificationTotackle with the intrinsic problem of overestimationfor the mode estimator, wepropose a no

48、ise injection based rectification method for an advanced estimation.It is clear that there is a relationship between the extent of overestimation andthe original image structures, as indicated by Figure 3. Larger variation of thelocal variance will result in larger mode of the distribution and subse

49、quently ahigher level of overestimation. Fortunately,the preliminary estimation result canbe used to acquire the rectification value because overestimation are inherent inthe preliminary results.2as the testHere we use the preliminary estimation of noise variance npre2noise variance nand generate a

50、test noise matrix according to the size oftest2original noisy image, with 0 mean and variance equals to n. Because thetestmode estimator is irrelevant to any specific distribution of the noise, a simple148C. Tang, X. Yang, and G. ZhaiGaussian noise matrix can be generated as the ntest. Then the test