报告承办单位:数学与统计学院

报告内容: Image restoration via the local adaptive TV-based regularization

报告人姓名: 庞志峰

报告人所在单位: 河南大学数学与统计学院

报告人职称/职务及学术头衔:副教授/硕导

报告时间: 2019年5月20日上午10:00—11:00

报告地点: 理科楼A419

报告人简介: 庞志峰博士，河南大学数学与统计学院副教授, 硕士生导师。目前任河南省数字图形图像学会常务理事和秘书长, 并分别兼任该学会的智能精准放疗专业委员会和智能信息融合专业委员会副主委, 同时任中国生物医学工程学会医学人工智能专委会青年委员会委员和中国工业与应用数学学会数学与医学交叉委员会委员。主要研究图像处理中的数学理论与数值算法。曾主持国家自然科学基金1项, 参与国家自然科学基金2项, 国家重点基础研究发展计划(973项目)1项。现发表相关学术论文27篇(其中SCI收录25篇), 授权专利1项。

报告摘要：Image denoising problem still remains an active research field in the image processing. In the proposed model, how to describe the local structure of image is very important to improve the denoising quality. This paper proposes an image denoising model based on the adaptive weighted TVp regularization, where the regularization term can efficiently depict local structures by coupling the rotation matrix and the weighted matrix into the TVp-quasinorm. The adaptive angle used in the rotation matrix via the orientation field estimation mainly depends on the average phase angle of pixels within a suitable window, so this approach is more reasonable to express the local structure information. In addition, since the proposed model is nonsmooth and non-Lipschitz, we employ the alternating direction method of multipliers (ADMM) to solve it based on the half-quadratic scheme for solving the related ℓ2 − ℓp subproblem. We prove the convergence of the half-quadratic scheme under the framework of the alternating direction method (ADM) with a gradually decreasing smooth parameter. Furthermore, we also discuss the convergence of the ADMM. Some numerical comparisons with the classic TV-based models illustrate the good performance of our proposed model for the image denoising problem.