报告题目： A TV-SCAD approach for image deblurring with impulsive noise
报告人：杨俊锋教授 （南京大学）
报告时间：11月22日（周五）下午：4：00-5：00
报告地点：数学楼307
报告摘要：We consider image deblurring problem in the presence of impulsive noise. It is known that total variation (TV) regularization with L1-norm penalized data fitting works reasonably well only when the level of impulsive noise is relatively low. For high level impulsive noise, TVL1 works poorly. The reason is that all data, both corrupted and noise free, are equally penalized in data fitting, leading to insurmountable difficulty in balancing regularization and data fitting. In this paper, we propose to combine TV regularization with nonconvex smoothly clipped absolute deviation (SCAD) penalty for data fitting. Our motivation is simply that data fitting should be enforced only when an observed data is not severely corrupted, while for those data more likely to be severely corrupted, less or even null penalization should be enforced. A difference of convex functions algorithm is adopted to solve the nonconvex TVSCAD model, resulting in solving a sequence of TVL1-equivalent problems, each of which can then be solved efficiently by the alternating direction method of multipliers. Theoretically, we establish global convergence to a critical point of the nonconvex objective function. The R-linear and at least sublinear convergence rate results are derived for the cases of anisotropic and isotropic TV, respectively. Numerically, experimental results are given to show that the TVSCAD approach improves those of the TVL1 significantly, especially for cases with high level impulsive noise, and is comparable with the recently proposed iteratively corrected TVL1 method.
This is a joint work with Prof. Guoyong Gu from Nanjing University.
Bio: Junfeng Yang, Professor, Department of Mathematics, Nanjing University. He is mainly interested in designing, analyzing and implementing robust and efficient algorithms for solving optimization problems arising from signaland image processing, compressive sensing and sparse optimization, and so on. Together with collaborators, he has developed Matlab packages FTVd for image deblurring and YALL1 for L1 problems in compressive sensing.
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