The application of non-convex rank approximation based on TV and gamma norm in matrix completion
WANG Shuqin1， WANG Yongli1， SUN Zhipeng1， HU Zixuan1， BIAN Xinxin1， HE Guoping2
1.College of Mathematics and Systems Science， Shandong University of Science and Technology， Qingdao， Shandong 266590，China；2.Shandong Academy of Science，Jinan 250000，China
Abstract：In real life， due to the influence of motion blur， optical blur and other factors， the observed image is often fuzzy and incomplete， that is， the image quality may be degraded and details are covered， which affects the visual effect and further applications. Matrix completion aims to recover a clean and complete image from the fuzzy and incomplete image with the greatest fidelity. In this paper， the gamma norm is used instead of the traditional nuclear norm as the non-convex approximation of the rank function. Compared with the nuclear norm， the gamma norm greatly weakens the contribution of the large singular value， and makes the contribution of the smaller singular value to close to zero. Meanwhile， the Total Variation (TV) regularization is exploited to preserve the edge structure and detail information of the image， so as to avoid the over smoothing of the recovered image. Then we use the augmented Lagrangian multiplier method to solve our proposed model. Finally， numerical experiments validate the proposed algorithm is more efficient than the existing algorithms for matrix completion.
王淑琴,王永丽,孙志鹏,胡子璇,边新新,贺国平. 基于TV与gamma范数的非凸秩近似在矩阵补全中的应用[J]. 华中师范大学学报(自然科学版), 2019, 53(6): 857-863.
WANG Shuqin,WANG Yongli,SUN Zhipeng,HU Zixuan,BIAN Xinxin,HE Guoping. The application of non-convex rank approximation based on TV and gamma norm in matrix completion. journal1, 2019, 53(6): 857-863.
2019, Vol. 53 
