报 告 人: 郭志昌(哈尔滨工业大学)

报告地点：腾讯会议: 449-148-963(无密码)

报告时间:   6月3日16:00-17:00

主办单位：数学与统计学院

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  报告摘要: Variational models involving Euler’s elastica energy have been widely used in many fields of digital image processing, such as image inpainting and additive Gaussian noise removal. In this paper, according to the signal dependence of multiplicative noise, the Euler’s elastica functional is modified to adapt for the multiplicative denoising problem. And a novel multiplicative noise removal model based on adaptive Euler’s elastica is proposed. Furthermore, we develope two fast numerical algorithms to solve this high-order nonlinear model: Aiming at the evolution case of Euler-Lagrange equation, a semi-implicit iterative scheme is designed and the additive operator splitting (AOS) algorithm is used to speed up the calculation; Expanding the augmented Lagrangian algorithm that has been successfully applied in recent years, we obtain a restricted proximal augmented Lagrangian method. Numerical experiments show the effectiveness of the two algorithms and the significant advantages of our model over the standard total variation denoising model in alleviating the staircase effect and restoring the tiny geometrical structures, especially, the line-like feature.

专 家简介: 郭志昌，哈尔滨工业大学数学学院副教授，博士生导师, 计算数学系副主任和计算数学研究所副所长，中国生物医学工程学会医学人工智能分会青年委员，主要分数阶方程的数值理论和在图像恢复中的建模，深度学习卷积神经网络的部分解释，基于PDE和深度学习卷积神经网络的融合模型等方面的研究。在SIAM系列和IEEE系列等高水平期刊上发表学术论文20余篇。现主持国家自然科学基金面上项目1项, 曾主持结项国家和省部级项目4项, 参与面上基金2项。