基于广义低秩矩阵分解的分离字典训练及其快速重建算法

doi:10.3969/j.issn.0372-2112.2018.10.013

电子学报 ›› 2018, Vol. 46 ›› Issue (10): 2400-2409.DOI: 10.3969/j.issn.0372-2112.2018.10.013

基于广义低秩矩阵分解的分离字典训练及其快速重建算法

张长伦, 余沾, 王恒友, 何强

北京建筑大学理学院, 北京 100044

收稿日期:2017-05-22 修回日期:2018-05-04 出版日期:2018-10-25
- 通讯作者:
- 王恒友
- 作者简介:
- 张长伦,男.1972年8月出生,山东济宁人.2005年毕业于北京交通大学电子信息与工程学院,取得工学博士学位.现为北京建筑大学理学院副教授,从事网络信息安全理论与应用研究、大数据分析、复杂网络理论研究等.E-mail:zclun@bucea.edu.cn;余沾,男.1993年6月出生,湖北荆州人.2015年毕业于北京建筑大学信息与计算科学系,取得理学学士学位.现为北京建筑大学理学院硕士研究生,从事压缩感知、低秩矩阵分解等有关方面研究.E-mail:2107010415004@stu.bucea.edu.cn
- 基金资助:
- 国家自然科学基金 (No.61502024，No.61473111）; 北京市教委科技计划 (No.SQKM201610016009）; 北京市属高校基本科研业务费专项 (No.X18086）; "建大英才"项目; 北京建筑大学北京未来城市设计高精尖创新中心开放课题 (No.UDC2017033322）; 北京建筑大学科研基金 (No.KYJJ2017026）

Separable Dictionary Training and Its Fast Reconstruction Algorithm Based on Generalized Low-Rank Matrix Approximation

ZHANG Chang-lun, YU Zhan, WANG Heng-you, HE Qiang

School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China

Received:2017-05-22 Revised:2018-05-04 Online:2018-10-25 Published:2018-10-25
- Corresponding author:
- WANG Heng-you
- Supported by:
- National Natural Science Foundation of China (No.61502024, No.61473111); Science and Technology Project of Beijing Municipal Education Commission (No.SQKM201610016009); Fundamental Scientific Research Fund for Universities of Beijing Municipality (No.X18086); Talent Program of Beijing University of Civil Engineering and Architecture; Open Project of Beijing Advanced Innovation Center for Future Urban Design of Beijing University of Civil Engineering and Architecture (No.UDC2017033322); Research Foundation of Beijing University of Civil Engineering and Architecture (No.KYJJ2017026)

摘要/Abstract

摘要： 针对传统压缩感知重建算法存在重建质量偏低、重建时间偏长等问题，本文提出了一种基于分离字典训练的快速重建算法.首先选取某类图像作为训练集，建立其广义低秩矩阵分解模型；其次采用交替方向乘子法求解该模型，训练出一组分离字典；最后将该分离字典用于图像重建中，通过简单的线性运算实现图像的快速重建.实验结果表明，本文算法相比于传统的重建算法，针对训练集同类图像，具有十分显著的重建性能，对于其他不同类型的图像，依然有不错的重建质量，极大地降低了重建时间.

关键词: 压缩感知, 广义低秩矩阵分解, 分离字典训练, 快速重建

Abstract: Since traditional compressive sensing reconstruction algorithms have lower reconstruction quality and longer running time, a fast reconstruction algorithm based on separable dictionary training is proposed. Firstly, we choose one class of images as training set and construct their models of generalized low-rank matrix approximation. Then, the alternating direction method is used to solve the model, and we can obtain separable dictionaries. Finally, the separable dictionaries are applied to image reconstruction and realize fast reconstruction of image by simple linear operation. The experimental results show that the proposed algorithm has a better reconstruction performance for training set images compared to traditional reconstruction algorithms. In addition, for other types of images, our algorithm has a good reconstruction quality and a lower reconstruction time.

Key words: compressive sensing, generalized low-rank matrix approximation, separable dictionary training, fast reconstruction

中图分类号:

TN911.7

张长伦, 余沾, 王恒友, 等. 基于广义低秩矩阵分解的分离字典训练及其快速重建算法[J]. 电子学报, 2018, 46(10): 2400-2409.

ZHANG Chang-lun, YU Zhan, WANG Heng-you, et al. Separable Dictionary Training and Its Fast Reconstruction Algorithm Based on Generalized Low-Rank Matrix Approximation[J]. Acta Electronica Sinica, 2018, 46(10): 2400-2409.

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基于广义低秩矩阵分解的分离字典训练及其快速重建算法

Separable Dictionary Training and Its Fast Reconstruction Algorithm Based on Generalized Low-Rank Matrix Approximation

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