Image denoising and deblurring: non-convex regularization, inverse diffusion and shock filter

作     者：FU ShuJun 1,2,3 , ZHANG CaiMing 2 & TAI XueCheng 3,4 1 School of Mathematics, Shandong University, Jinan 250100, China 2 School of Computer Science and Technology, Shandong University, Jinan 250101, China 3 School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798, Singapore 4 Department of Mathematics, University of Bergen, Bergen 5008, Norway 

作者机构：School of Mathematics Shandong University School of Computer Science and Technology Shandong University School of Physical and Mathematical Sciences Nanyang Technological University Department of Mathematics University of Bergen 

出 版 物：《Science China(Information Sciences)》 (中国科学:信息科学(英文版))

年 卷 期：2011年第54卷第6期

页      面：1184-1198页

核心收录：

学科分类：0810[工学-信息与通信工程] 0808[工学-电气工程] 08[工学] 080203[工学-机械设计及理论] 0802[工学-机械工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the MOE(Ministry of Education)Tier II Project(Grant No.T207N2202) the IDM Project(Grant No.NRF2007IDM-IDM002-010) the National Natural Science Foundation of China(Grant Nos.60933008,61070094,61020106001) the China Postdoctoral Science Foundation(Grant No.20090460089) the support from SUG20/07 

主　　题：image denoising image deblurring non-convex regularization inverse diffusion shock filter adaptive anisotropic diffusion 

摘      要：A large number of applications in image processing and computer vision depend on image quality. In this paper, main concerns are image denoising and deblurring simultaneously in a restoration task by three types of methodologies: non-convex regularization, inverse diffusion and shock filter. We discuss their relations in the context of image deblurring: the inverse diffusion implied by the non-convex regularization, and the superior ability of deblurring edge of the shock filter to that of the inverse diffusion, both in 1D and 2D cases. Finally, we propose a region-based adaptive anisotropic diffusion with shock filter method, which shows advantages of deblurring edges, denoising and smoothing contours in experiments, compared with some related methods. Therein an idea of divide and rule is introduced.