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基于高阶奇异值分解和均方差迭代的图像去噪

DOI: 10.11834/jig.20141102

Keywords: 高阶奇异值分解,均方差,非局部协同滤波,数据自适应

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Abstract:

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。

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