实现数字图像中噪声参数的精确估计对提高图像处理的质量有重要意义。对被高斯白噪声所污染的图像进行稀疏主成分分析时, 其部分主成分的负载向量的均值与高斯白噪声标准差呈现一定的线性关系。基于此特征, 本文提出了一种快速精确的图像噪声估计方法。在该方法中, 通过对高斯白噪声污染图像添加多种已知标准差等级的新的高斯白噪声以产生多幅新图像, 然后对每幅图像进行稀疏主成分分析, 并求取多个主成分负载向量均值。最后, 通过求解一个超定方程组实现图像高斯噪声标准差等级的精确估计。实验结果表明, 本方法在低噪声(δ0=5)到高噪声(δ0=70)条件下均具有较高的估计精度和较强的鲁棒性, 在实际工程中具有一定的实用价值。

Realizing accurate estimation of noise parameters in digital images is of great significance for improving the quality of image processing. When the sparse principal component analysis is performed on the image contaminated by Gaussian white noise, the mean value of the load vector of some principal components and the standard deviation of Gaussian white noise show a certain linear relationship. Based on this feature, this paper proposes a fast and accurate image noise estimation method. In this method, a plurality of new Gaussian white noises of known standard deviation levels are added to the Gaussian white noise-contaminated image to generate a plurality of new images, and then each sample is subjected to sparse principal component analysis and mean of multiple principal component load vectors are obtained. Finally, an accurate estimation of the standard deviation of Gaussian noise is achieved by solving an over determined system of equations. The experiment results show that the method has high estimation accuracy under low noise (δ0=5) to high noise (δ0=70) conditions, and strong robustness is demonstrated. This method has certain practical value in practical engineering.