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統計學院專家報告:江蘇師范大學賈志剛教授學術報告

福彩浙江快乐彩浙江快乐彩开奖结果查询 www.gaeib.com 發布日期 : 2019-06-04 瀏覽次數 :

報告題目:Robust quaternion matrix completion with applications to image inpainting

報告摘要In this paper, we study robust quaternion matrix completion and provide a rigorous analysis for provable estimation of quaternion matrix from a random subset of their corrupted entries. In order to generalize the results from real matrix completion to quaternion matrix completion, we derive some new formulas to handle noncommutativity of quaternions. We solve a convex optimization problem, which minimizes a nuclear norm of quaternion matrix that is a convex surrogate for the quaternion matrix rank, and the 1 -norm of sparse quaternion matrix entries. We show that, under incoherence conditions, a quaternion matrix can be recovered exactly with overwhelming probability, provided that its rank is sufficiently small and that the corrupted entries are sparsely located. The quaternion framework can be used to represent red, green, and blue channels of color images. The results of missing/noisy color image pixels as a robust quaternion matrix completion problem are given to show that the performance of the proposed approach is better than that of the testing methods, including image inpainting methods, the tensor-based completion method, and the quaternion completion method using semidefinite programming.

報告時間2019年6月14日10:00—11:00

報告地點:統計學院213會議室

專家簡介:賈志剛 ,江蘇師范大學教授、碩士生導師。2009年畢業于華東師范大學數學系,獲理學博士學位。主要研究方向為數值代數與圖像處理,至今已在SIAM J. Matrix Anal. Appl., SIAM J. Imaging Sci., J. Sci. Comput., Numer. Linear Algebra Appl.等國際知名期刊上發表學術論文30余篇,出版譯著1部、教材1部,主持國家自然科學基金項目2項、省部級科研項目1項,參加國家和省自然科學項目4項。先后入選江蘇師范大學“第一批高層次人才隊伍后備人選”、“三育人先進個人”、“校先進工作者”等。曾經到英國曼徹斯特大學、香港浸會大學等高校數學系進行為期一年的訪問。現兼職為中國高等教育學會教育數學專業委員會團體理事、江蘇省工業與應用數學會理事、江蘇省計算數學學會理事、美國SIAM正式會員,美國Math Review評論員,和SIMAX,Inverse Problem,Automatic等學術期刊的審稿人。

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