目的 图像去噪是图像处理的难题,其难点是在尽量滤除噪声的同时对图像信息进行保持。针对该难点,本文提出了一种将非局部相似性和高阶奇异值分解(HOSVD)相融合,并利用均方差(MSE)迭代对图像进行去噪的iHOSVD算法。方法 首先利用非局部相似块聚类和高阶奇异值分解构建数据自适应的3维变换基及其变换系数;其次,对变换系数进行阈值处理后进行3维反变换,从而达到非局部协同滤波的目的;最后,由于一次去噪操作无法达到理想的去噪效果,采用一种基于均方差最优的迭代方法对图像进行去噪,并证明该迭代是一个权衡偏差和方差使得均方差达到最优的过程。结果 实验结果表明,iHOSVD算法既能够有效地去除噪声,又能够很好地保持纹理细节信息。结论 本文所提的图像去噪iHOSVD算法结合了非局部协同滤波与数据自适应去噪的思想,通过对3种高水平去噪算法BM3D、NCSR和PLOW的比较实验发现,不仅表现了较强的图像去噪能力,而且在图像纹理细节保持方面效果最好,适用于纹理信息较强的图像。
Image denoising based on high order singular value decomposition and mean square error iteration
Objective The challenge of image denoising is how to filter the noise as more as possible while preserve the image information at the same time. To reduce this contradiction, we propose an iterative image denoising method by combining the non-local techniques and the high order singular value decomposition (HOSVD). Method Our method first uses the non-local patch clustering and the HOSVD to construct the data-adaptive 3D transform basis and coefficients. Then an inverse transformation is taken to get the denoised patches after filtering the coefficients by a threshold value. Usually, denoising once is not enough to get the desired denoised result. Therefore, we design an iterative denoising strategy for the proposed method, which is verified to be a process to take the trade-off between bias and variance and optimize the mean square error (MSE). Result Experiments illustrate that our method not only filter the noise effectively but also preserve the texture well. Conclusion Our method combines advantages of both non-local collaborative filtering and data-adaptive denoising. Compared with the other three advanced denoising methods, such as, BM3D, NCSR and PLOW, our method outperforms them in terms of texture preserving.