提出一种利用小波变换子图像不同的方向特性和峰值信噪比进行奇异值分解的图像去噪算法。由于图像经过小波变换后,低频子图像集中了原图像的大部分能量噪声,故仅作简单维纳滤波；而噪声则主要集中在小波域中的三个不同方向的高频子图中,且系数较小,因此可以利用奇异值分解进行去噪处理,即用较大的奇异值和对应的特征向量重构出去噪图像,然而由于奇异值分解固有的行列方向性,对于高频对角线子图重构出的图像去噪效果不理想,故采取旋转至行列方向后再进行常用的奇异值滤波；最后将去噪后的低频和高频子图进行小波反变换重构出最终的去噪图像,其中重构所需的奇异值个数由图像的峰值信噪比确定。 实验结果表明,该方法在有效去噪的同时较好的保留了原有的高频细节信息。

An optimized image singular value decomposition (SVD) denoising algorithm based on wavelet transform directional information and peak signal to noise ratio (PSNR) was proposed. As most of the energy noises were concentrated in low-frequency sub-image after wavelet transform, the simple Wiener filtering was made; on the other hand, the image noises were mainly concentrated in the high-frequency sub-image with three different directions and the coefficient was smaller, so the larger singular values of SVD and their corresponding eigenvectors were used to reconstruct denoising image; however, because of the inherent directional feature of the SVD, the denoising result of image reconstructed from high-frequency diagonal sub-image was not satisfied, so the diagonal sub-image was rotated to the level (vertical) direction, then the SVD filtering was done; finally, the anti-wavelet transform was used to reconstruct the denoising image based on the low-frequency and high-frequency sub-images, and the required number of singular values was determined by PSNR of the image. Experimental results show that this method has effective denoising effect, while retaining the high-frequency original details.