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基于L0范数正则项的运动图像去模糊

Motion Image Deblurring Based on L0 Norms Regularization Term

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摘要

针对运动模糊图像的模糊去除问题, 提出了一种基于L0范数正则化的模糊核方法。该方法以图像梯度L0范数为正则项, 根据图像的稀疏先验条件, 选取合适的参数估计方法, 构建了一个非凸的最优化能量函数。在对该函数进行数值求解中, 选用了交替迭代法, 交替更新原始图像和模糊核的估计值。在原始图像估计中, 以图像梯度L0范数为稀疏正则项可以有效地保留图像的强边缘并抑制弱边缘对模糊核估计的影响, 从而提高了核估计的正确率。在模糊核计算过程中, 模糊核估计最优化能量函数则转换为一个经典的凸优化问题, 再通过对能量函数进行快速傅里叶变换计算可以快速得到所需的估计模糊核。在成功估计出图像模糊核后, 图像的盲去卷积问题就转换为图像的非盲反卷积问题。采用以L0.5为正则项的超拉普拉斯先验算法进行反卷积, 该算法能够逼近自然图像的重尾分布从而获得更佳的复原结果。实验结果证明, 提出的图像去模糊算法与其他近似方法相比, 去模糊效果更佳。

Abstract

Aiming at the problem of motion image deblurring, a fuzzy kernel method based on L0 norms regularization term is presented. This method applies the image gradient L0 norms as the regularization term to construct a non-convex optimization energy function through the sparse prior condition of the image and the appropriate parameter estimation method. In the process of solving the function, the alternating iteration method is used to update the original image and the estimated values of the fuzzy kernel. In the process of original image estimation, the sparse regularization term of the image gradient L0 norms can effectively retain the sharp edges as well as suppress the influence of the weak edges on the fuzzy kernel estimation, which can obviously improve the accuracy of kernel estimation. In the process of fuzzy kernel calculation, the optimization energy function of fuzzy kernel converts to a classic convex optimization. Using the fast Fourier transform to compute the energy function can quickly get the estimated kernel. After getting the appropriate kernel of image, the problem of image blind deconvolution can be converted to the image non-blind deconvolution. A hyper-Laplacian priors using L0.5 as the regularization term is applied in deconvolution. This algorithm can well model the heavey-tailed distribution of gradients in natural scenes so that a perfect result can be obtained. Experimental results demonstrate that the proposed method gets higher quality deblurring results than the previous methods.

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中图分类号:TN911.73

DOI:10.3788/lop54.021005

所属栏目:图像处理

基金项目:国家自然科学基金(61672335)、国家自然科学基金青年科学基金(61601276)、广东省自然科学基金(2016A030310077)、汕头职业技术学院基金(SZK2016Y13)

收稿日期:2016-09-23

修改稿日期:2016-10-10

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闫敬文:汕头大学工学院, 广东 汕头 515063
谢婷婷:汕头大学工学院, 广东 汕头 515063
彭鸿:汕头职业技术学院机电工程系, 广东 汕头 515073
刘攀华:汕头大学工学院, 广东 汕头 515063

联系人作者:闫敬文(jwyan@stu.edu.cn)

备注:闫敬文(1964-), 男, 博士, 教授, 博士生导师, 主要从事超小波分析、压缩感知方面的研究。

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引用该论文

Yan Jingwen,Xie Tingting,Peng Hong,Liu Panhua. Motion Image Deblurring Based on L0 Norms Regularization Term[J]. Laser & Optoelectronics Progress, 2017, 54(2): 021005

闫敬文,谢婷婷,彭鸿,刘攀华. 基于L0范数正则项的运动图像去模糊[J]. 激光与光电子学进展, 2017, 54(2): 021005

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