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
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