基于PCA的图像小波去噪方法

目前使用的各种小波去噪方法基本上都是建立在对噪声方差精确估计的基础上，而对噪声方差的精确估计是很困难的．提出了一种采用主分量分析（PCA）提取小波系数的主要特征，通过对小波域中噪声能量的估计来实现去噪的新方法．首先利用PCA对小波高频子带进行局部特征提取；然后以主分量对小波系数进行重建的平均能量作为局部噪声能量的估计；将原小波系数的能量减去噪声能量，就得到去噪后的小波系数；最后用小波逆变换对剔除噪声分量后的小波系数进行恢复得到去噪后的图像．本文算法无需对噪声方差进行估计，因而更具实用价值．本文算法与“软阈值”、“硬阈值”去噪方法相比，峰值信噪比（PNNR）提高了2～8dB．实验证实了本文算法良好的去噪性能。

Wavelet Image Denoising Based on Principle Component Analysis

Most of the existing methods on wavelet image denoising rely on accurate estimation of noise variance. In practice, however, the estimation of noise variance is very hard. To overcome this difficulty, this paper proposes a new method which utilizes noise energy, instead of its variance, to perform image denoising based on Principle Component Analysis (PCA) in the wavelet domain. First, wavelet decomposition is conducted on the noisy image, and PCA is used to extract local features; Second, the wavelet coefficients are reconstruct based on the top few principle components and the local noise energy is estimated based on the mean energy of reconstructed wavelet coefficients; Third, noise energy is subtracted from the original wavelet coefficients, which results in denoised wavelet coefficients; Finally, the inverse wavelet transform is performed to obtain the denoised image. A unique feature of the new algorithm is that it does not rely on the difficult task of noise variance estimation. It is therefore of great value in solving real-world problems. Compared with the commonly-used wavelet hard-threshholding and soft-thresholing methods, the new algorithm increases the PSNR by 2-8dB. Extensive experiments are conducted and the results demonstrate the superior denoising performance of the proposed algorithm.