半张量积低存储压缩感知方法研究

doi:10.3969/j.issn.0372-2112.2018.04.005

电子学报 ›› 2018, Vol. 46 ›› Issue (4): 797-804.DOI: 10.3969/j.issn.0372-2112.2018.04.005

半张量积低存储压缩感知方法研究

王金铭, 叶时平, 徐振宇, 陈超祥, 蒋燕君

浙江树人大学信息科技学院, 浙江杭州 310015

收稿日期:2017-03-29 修回日期:2017-09-04 出版日期:2018-04-25
- 作者简介:
- 王金铭 男.1978年10月出生,浙江富阳人.2005年于浙江大学获硕士学位,副教授.主要从事非线性信息处理、图像处理、压缩感知等方面的研究工作.E-mail:wjm7878@163.com;叶时平 男.1967年1月出生,浙江丽水人.浙江树人大学教授.主要从事图像处理、智能系统、地理信息系统等方面的研究工作.E-mail:zjsruysp@163.com
- 基金资助:
- 浙江省自然科学基金 (No.LY14E070001）; 浙江省公益技术应用研究计划 (No.2015C33074，No.2015C33083）; 浙江省科技计划 (No.2014C33058）

Low Storage Space of Random Measurement Matrix for Compressed Sensing with Semi-tensor Product

WANG Jin-ming, YE Shi-ping, XU Zhen-yu, CHEN Chao-xiang, JIANG Yan-jun

College of Information Science & Technology, Zhejiang Shuren University, Hangzhou, Zhejiang 310015, China

Received:2017-03-29 Revised:2017-09-04 Online:2018-04-25 Published:2018-04-25
- Supported by:
- National Natural Science Foundation of Zhejiang Province, China (No.LY14E070001); Public Welfare Technology Application Research of Zhejiang Province (No.2015C33074, No.2015C33083); Science and Technology Project of Zhejiang Province (No.2014C33058)

摘要/Abstract

摘要： 由于随机观测矩阵的随机性，存在数据存储量大、内存占用率高、数据计算量大以及难以面向大规模实际应用等问题.为此，提出了一种可有效降低随机观测矩阵所占存储空间的半张量积压缩感知（STP-CS）方法.利用该方法，构建低维随机观测矩阵，经奇异值分解（SVD）优化后对原始信号进行采样，并利用拟合0-范数的迭代重加权方法进行重构.实验利用2维灰度图像进行测试，并对重构图像的峰值信噪比，结构相似度等指标进行了统计和比较.实验结果表明，本文所述的STP-CS方法在不改变随机观测矩阵数据类型的前提下，可将观测矩阵减小至传统CS模型中观测矩阵所占内存空间的1/256（甚至更低），同时仍保持很高的重构质量.

关键词: 压缩感知, 随机观测矩阵, 半张量积, 存储空间, 奇异值分解

Abstract:

Random measurement matrix needs large storage space, huge memory requirements for reconstruction, and high computational cost, which are not suitable for large-scale applications. To reduce the storage space of random measurement matrix for compressed sensing (CS), a new sampling approach for CS with semi-tensor product (STP-CS) is proposed. The STP-CS approach generates a random matrix, where the row and column numbers of the matrix are smaller than that for conventional CS. Then we optimize the matrix by the singular value decomposition (SVD) approach, after sampling with the matrix, we estimate the solutions of the sparse vector with the smooth l₀-norm minimization algorithm. Numerical experiments were conducted using gray-scale images, the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM) of the reconstruction images were compared with the random matrices with different dimensions. Comparisons were also conducted with other random measurement matrix and other low storage techniques. Numerical experiment results show that the STP-CS can effectively reduce the storage space of the random measurement matrix to 1/256 of that for conventional CS, while maintaining the reconstruction performance.

Key words: compressed sensing, random measurement matrix, semi-tensor product (STP), storage space, singular value decomposition (SVD)

中图分类号:

TN911.73

王金铭, 叶时平, 徐振宇, 等. 半张量积低存储压缩感知方法研究[J]. 电子学报, 2018, 46(4): 797-804.

WANG Jin-ming, YE Shi-ping, XU Zhen-yu, et al. Low Storage Space of Random Measurement Matrix for Compressed Sensing with Semi-tensor Product[J]. Acta Electronica Sinica, 2018, 46(4): 797-804.

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半张量积低存储压缩感知方法研究

Low Storage Space of Random Measurement Matrix for Compressed Sensing with Semi-tensor Product

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