報(bào)告人：任歡 博士

報(bào)告題目：Quaternion matrix completion with total variation regularization utilizing fast dual proximal gradient method

報(bào)告時(shí)間：2025年12月6日（周六）下午4：00

報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓304會(huì)議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

任歡，博士，講師，碩士生導(dǎo)師。主要從事數(shù)值代數(shù)、數(shù)值優(yōu)化、數(shù)據(jù)科學(xué)等領(lǐng)域的研究，在低秩逼近、矩陣及張量恢復(fù)、圖像科學(xué)、非線性矩陣方程、互補(bǔ)問(wèn)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?yàn)榫仃嚰皬埩炕謴?fù)問(wèn)題及其在圖像處理中的應(yīng)用。迄今為止主持國(guó)家自然科學(xué)基金項(xiàng)目1項(xiàng)、江西省自然科學(xué)基金項(xiàng)目1項(xiàng)、江西省職業(yè)早期青年科技人才培養(yǎng)項(xiàng)目1項(xiàng)。近年來(lái)以第一作者在J. Sci. Comput., Calcolo, Numer. Algor., Comput. Math. Appl., Comput. Appl. Math.等國(guó)際權(quán)威期刊上發(fā)表多篇論文。目前擔(dān)任了Appl. Math. Lett., Comput. Math. Appl., Comput. Appl. Math., Filomat等國(guó)際知名期刊審稿人。

報(bào)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.