题    目：Quaternion Tensor Completion via QR Decomposition and Nuclear Norm Minimization

主讲人：张扬 教授

单    位：加拿大曼尼托巴大学

时    间：2024年11月4日 15:00

地    点：学院二楼会议室

摘    要：The task of tensor (matrix) completion has been widely used in the fields of computer vision and image processing, etc. To achieve the completion, the existing methods are mostly based on singular value decomposition of the real tensors and nuclear norm minimization. However, the real tensor completion methods cannot simultaneously maintain color channel correlation and evolution robustness of color video frames, and they need high computational costs to handle the high-dimensional data. Hence they have some limitations in model generalization ability and computational efficiency. In this paper, a new completion method for the quaternion tensor (matrix) is explored via the QR decomposition and the definition of novel quaternion tensor norm, which can well balance the model generalization ability and efficiency, and the performance of the completion method has been substantially improved. Numerical experiments on color images and videos prove the effectiveness of our proposed method.

简    介：张扬，加拿大曼尼托巴大学教授。主要研究方向是环理论，计算机代数，自动推理证明，矩阵和张量理论，包括斜多项式分解， Groebner 基理论，求解矩阵和张量方程，他的研究得到了加拿大国家自然科学和工程基金(NSERC)连续支持。现任NSERC基金计算机委员会会评成员。