Low-Rank Quaternion Matrix and Tensor Function Representation with Applications in Color Image Processing

江苏省应用数学（中国矿业大学）中心系列学术报告

报告题目：Low-Rank Quaternion Matrix and Tensor Function Representation with Applications in Color Image Processing

报告人：汪祥 教授单位：南昌大学数学与计算机学院

报告时间：2026年10月17日（周六）上午 10:30-11:30

报告地点：数学学院A321

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报告人及报告内容简介：

汪祥，教授，博士生导师，宝钢优秀教师奖获得者，担任国家天元数学东南中心江西基地负责人，中国数学会计算数学分会理事，中国高等教育学会教育数学专委会常务理事, 国际知名期刊《Computational and Applied Mathematics》的AE。

汪祥教授长期从事数值代数、人工智能与数据科学等领域的研究，在大规模稀疏线性方程组、大规模稀疏特征值问题、线性和非线性矩阵方程的数值求解、谱聚类等方面取得了一些成果。目前主持(含完成)国家自然科学基金4项及省部级项目（含江西省杰出青年基金、江西省自然科学基金重点、重大项目）十几项。近几年以第一作者或通讯作者在Pattern Recognition, Advance in Computational Mathematics, Journal of Scientific Computing,Communications in Computational Physics等国际权威期刊上共发表SCI收录论文多篇。以第一完成人身份获江西省自然科学奖和江西省教学成果奖4项。

Abstract: As an innovative approach to color video recovery, low-rank quaternion tensor completion(LRQTC) representsa color video as a unified quaternion structure to characterize the correlations among RGB channels. However, most existing methods rely on low-rank decomposition strategies based on discrete factor structures, which have inherent limitations in capturing global correlations that vary with spatiotemporal coordinates. In addition, traditional smoothness priors are usually constructed based on pixel-level gradients, ignoring thedistinct characteristics of saturation and value variations in color data. To overcome these limitations, this paper proposes a low-rank quaternion tensor function representation method, whichexploits the implicit continuity of neural networks to more accurately characterize the discrete quaternion tensor structure of colorvideos. On this basis, a spatiotemporal SVTV (STSVTV) regularization term driven by neural representation introduced to capture global spatiotemporal correlations in a unified continuous domain, thereby promoting spatial smoothness and temporal consistency. Moreover, we prove that the proposed quaternion tensorcompletion model admits at least one solution and can be stably solved by an iterative gradient descent method. Numerical experiments demonstrate that, under different sampling rates and various spatial and temporal missing patterns, the proposed method achieves significantly superior recovery performance compared with several state-of-the-art methods.