報告人：任歡 博士
報告題目：Quaternion matrix completion with total variation regularization utilizing fast dual proximal gradient method
報告時間：2025年12月6日（周六）下午4：00
報告地點：云龍校區(qū)6號樓304會議室
主辦單位：數(shù)學與統(tǒng)計學院、數(shù)學研究院、科學技術(shù)研究院
報告人簡介：
任歡，博士，講師，碩士生導師。主要從事數(shù)值代數(shù)、數(shù)值優(yōu)化、數(shù)據(jù)科學等領(lǐng)域的研究，在低秩逼近、矩陣及張量恢復、圖像科學、非線性矩陣方程、互補問題的數(shù)值求解算法方面有較為深入的研究，且取得了一定的成果。目前主要研究方向為矩陣及張量恢復問題及其在圖像處理中的應用。迄今為止主持國家自然科學基金項目1項、江西省自然科學基金項目1項、江西省職業(yè)早期青年科技人才培養(yǎng)項目1項。近年來以第一作者在J. Sci. Comput., Calcolo, Numer. Algor., Comput. Math. Appl., Comput. Appl. Math.等國際權(quán)威期刊上發(fā)表多篇論文。目前擔任了Appl. Math. Lett., Comput. Math. Appl., Comput. Appl. Math., Filomat等國際知名期刊審稿人。
報告摘要：
Quaternion matrix completion aims to recover the original image from incomplete image data which has attracted attention in the fields of image and signal processing recently. Unlike traditional algorithms that only consider low-rankness of recovered image, We propose a novel algorithm that combines the Geman function and anisotropic or isotropic total variation (TV) regularization. In the process of solving the model by Alternating direction method of multipliers (ADMM) algorithm, we also employ the fast dual proximal gradient method to address the corresponding sub-problem about the TV regularization. The numerical results on color images demonstrate the effectiveness and reliability of the proposed algorithm.