散焦模糊图像复原的截断奇异值分解算法

散焦模糊图像复原的截断奇异值分解算法 Blurred Defocused Image Restoration Based on Truncated Singular Value Decomposition 朱华平 ZHU Huaping 1 first-author 吴传生 WU Chuansheng 1 周俊 ZHOU Jun 1 高飞 GAO Fei 1 武汉理工大学理学院 武汉理工大学理学院 School of Sciences,Wuhan University of Technology School of Sciences,Wuhan University of Technology 在反射边界条件假设下,导出了散焦和噪声所导致的图像降质的离散延拓模型,给出了延拓模型的卷积方程及相应的卷积算子;通过引进延拓矩阵的Fourier变换证明了该卷积算子的相关性质并导出了该卷积算子的奇异系,给出了一个解决散焦模糊图像复原的截断奇异值分解算法及算法的计算步骤.图像复原的数值实验实例表明了该算法的有效性. In this paper,a discrete extension model of the degraded images caused by defocus blurring and random noise is proposed under the assumption of reflecting boundary conditions by introducing the convolution equations and corresponding convolution operators of the discrete extension model. We prove the related properties and derive the singular system of the convolution operators by using the Fourier transform of the introduced extended matrix rigorously and propose a truncated singular value decomposition （TSVD） algorithm and its calculation steps to restore the defocus blurred images effectively. Then the numerical experiments of images restoration demonstrate the effectiveness of the algorithm. 图像复原 不适定问题 卷积 截断奇异值分解 image restoration ill-posed problems deconvolution truncated singular value decomposition （TSVD） 10.14188/j.1671-8836.2010.04.019 TP391.41 国家自然科学基金资助项目（60974094）;湖北省自然科学基金资助项目（2009CBD213） 2010-04-01 2021-04-01 4 56