基于回歸分析和主成分分析的噪聲方差估計方法
doi: 10.11999/JEIT170624
基金項(xiàng)目:
國家自然科學(xué)基金(11641002)，榆林市科技計劃項(xiàng)目(Gy13-12)，陜西省教育廳科研項(xiàng)目(11JK0636)
Noise Variance Estimation Method Based on Regression Analysis and Principal Component Analysis
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(College of Information Engineering, Yulin University, Yulin 719000, China)
Funds:
The National Natural Science Foundation of China (11641002), The Science and Technology Program of Yulin (Gy13-12), The Program of Education Commission of Shaanxi Province (11JK0636)
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摘要: 準(zhǔn)確可靠的噪聲強(qiáng)度估計是數(shù)字圖像處理領(lǐng)域中一個重要的研究課題。噪聲估計的難點(diǎn)在于如何提取用于估計的純噪聲信息，近幾年，許多算法采用主成分分析技術(shù)來避免圖像紋理信息的干擾，用最小特征值來估計噪聲方差，可以有效地減少圖像紋理信息對估計結(jié)果的影響，所以這類方法對于高頻圖像(豐富紋理圖像)效果很好。由于圖像塊數(shù)量有限，最小特征值實(shí)際上比真實(shí)噪聲方差小，而且圖像塊數(shù)量越少，偏差越大。如果直接把最小特征值作為估計方差，則容易低估計高噪聲。該文通過回歸分析確定最小特征值跟真實(shí)噪聲方差的比值和圖像塊數(shù)量呈冪函數(shù)關(guān)系，因此可以通過最小特征值和冪函數(shù)關(guān)系得到真實(shí)的噪聲方差。實(shí)驗(yàn)表明該文方法既能處理高頻圖像，又適合各種噪聲水平，同時也能處理乘性高斯噪聲。Abstract: Accurate and reliable blind noise estimation is an important research topic of digital image processing. The main challenge is how to extract pure noise information for estimating. In recent years, many algorithms use principal component analysis technology to exclude the interference of image textures information, and estimate noise level by using the minimal eigenvalue. So that, the image textures have smallest effect on the minimal eigenvalue, thus this kind of methods performs well for high frequency image (image with abundant textures). The minimal eigenvalue is actually smaller than the true noise variance because of limited image blocks, and the bias is the bigger if the number of image patches is the smaller. If the noise level is estimated as the smallest eigenvalue, the final result will be underestimated. It is found that the relation between the ratio of estimated result to real noise variance and the number of image blocks is power function by using regression analysis, thus the true noise level can be computed by using the minimal eigenvalue and the power function. The experiment results show that the proposed algorithm works well over a large range of visual content and noise conditions, and can process multiply Gaussian noise too.
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Key words:
- Noise image /
- Gaussian noise /
- Noise estimation /
- Principal component analysis /
- Regression analysis
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