刘涵,
黄开宇,
苏立玉
1.西安交通大学电子与信息工程学院 西安 710049
2.西安交通大学智能网络与网络安全教育部重点实验室 ??西安 ??710049
基金项目:国家自然科学基金(61573276)
详细信息
作者简介:刘静：女，1975年生，教授，博士生导师，从事压缩感知、图像融合、雷达信号处理方向的研究
刘涵：女，1991年生，硕士生，研究方向为压缩感知、图像处理、矩阵补全
黄开宇：男，1992年生，博士生，研究方向为压缩感知、信号处理、信号与图像处理
苏立玉：男，1996年生，硕士生，研究方向为压缩感知、图像处理、张量补全
通讯作者:刘静 elelj20080730@gmail.com
中图分类号:TP391.41计量
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被引次数:0
出版历程
收稿日期:2018-11-23
修回日期:2019-05-07
网络出版日期:2019-05-20
刊出日期:2019-11-01
Automatic Rank Estimation Based Riemannian Optimization Matrix Completion Algorithm and Application to Image Completion
Jing LIU,,Han LIU,
Kaiyu HUANG,
Liyu SU
1. School of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China
2. Ministry of Education Key Laboratory for Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an 710049, China
Funds:The National Natural Science Foundation of China (61573276)
摘要
摘要:矩阵补全(MC)作为压缩感知(CS)的推广，已广泛应用于不同领域。近年来，基于黎曼优化的MC算法因重构精度高、计算速度快的特点，引起了广泛关注。针对基于黎曼优化的MC算法需假设原矩阵秩固定已知，且随机选择迭代起点的特点，该文提出一种基于自动秩估计的黎曼优化MC算法。该算法通过优化包含秩正则项的目标函数，迭代获取秩估计值和预重构矩阵。在估计所得秩对应的矩阵空间上以预重构矩阵为迭代起点，利用基于黎曼流形的共轭梯度法进行矩阵补全，从而提高重构精度。实验结果表明，与几种经典的图像补全方法相比，该文算法图像重构精度显著提高。
关键词:图像补全(IC)/
矩阵补全(MC)/
自动秩估计/
黎曼优化/
卷积神经网络
Abstract:As an extension of Compressed Sensing(CS), Matrix Completion(MC) is widely applied to different fields. Recently, the Riemannian optimization based MC algorithm attracts a lot of attention from researchers due to its high accuracy in reconstruction and computational efficiency. Considering that the Riemannian optimization based MC algorithm assumes a fixed rank of the original matrix, and selects a random initial point for iteration, a novel algorithm is proposed, namely automatic rank estimation based Riemannian optimization matrix completion algorithm. In the proposed algorithm, the estimate of rank is obtained minimizing the objective function that involving the rank regulation, in addition, the iterative starting point is optimized based on Riemannian manifold. The Riemannian manifold based conjugate gradient method is then used to complete the matrix, thereby improving the reconstruction precision. The experimental results demonstrate that the image completion performance is significantly improved using the proposed algorithm, compared with several classical image completion methods.
Key words:Image Completion(IC)/
Matrix Completion(MC)/
Automatic rank estimation/
Riemannian optimization/
Convolutional Neural Network (CNN)
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