基于特征值反问题下的图像修复  

Image Restoration Based on Inverse Eigenvalue Problem

作　　者：程鹏 陈伟 CHENG Peng;CHEN Wei(College of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《河南教育学院学报（自然科学版）》2022年第4期15-22,26,共9页Journal of Henan Institute of Education(Natural Science Edition)

基　　金：河南省自然科学基金(BK20151299)。

摘　　要：图像的分割与修复是图像识别技术的关键所在。图像数据在计算机中以矩阵的形式存在,结合特征值反问题对缺损图像所生成的缺损矩阵进行修复。首先提出两类新的特征值反问题,提供唯一解证明的方法;其次将问题的解法应用于缺失图像的修复并分析图像修复的效果。The image segmentation and restoration are the key to image recognition technology. Image data exists in the form of a matrix in the computer. Combined the inverse eigenvalue problem to repair the defect matrix generated by the defect image. First, two new types of eigenvalue inverse problems were proposed, and a method of proof of the unique solution was given. Secondly, applied the solution of the problem to the repair of the missing image and analyzed the effect of the image repair.

关 键 词：特征值反问题 实对称带状矩阵 JACOBI矩阵 正交矩阵 图像修复 Householder变换 

分 类 号：O241.6[理学—计算数学] TP751[理学—数学]