半张量积压缩感知模型的快速重构方法

王金铭; 叶时平; 尉理哲; 许森; 蒋燕君

doi:10.11959/j.issn.1000-436x.2018111

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半张量积压缩感知模型的快速重构方法

学术论文 | 更新时间：2024-06-05

- 半张量积压缩感知模型的快速重构方法
- Fast reconstruction method for compressed sensing model with semi-tensor product
- 通信学报 2018年39卷第7期页码：26-38
- 作者机构：
  
  浙江树人大学信息科技学院，浙江杭州 310015
- 作者简介：
  
  [ "王金铭（1978-），男，浙江富阳人，浙江树人大学副教授，主要研究方向为非线性信息处理、图像处理、压缩感知等。" ]
  [ "叶时平（1967-），男，浙江丽水人，浙江树人大学教授，主要研究方向为图像处理、智能系统、地理信息系统等。" ]
  [ "尉理哲（1983-），女，内蒙古呼伦贝尔人，浙江树人大学讲师，主要研究方向为车联网、WSN、深度学习等。" ]
  [ "许森（1982-），男，湖北荆门人，浙江树人大学讲师，主要研究方向为人工智能、智能控制、物联网等。" ]
  [ "蒋燕君（1973-），男，浙江诸暨人，博士，浙江树人大学教授，主要研究方向为智能电网、图像处理等。" ]
- 基金信息：
  
  浙江省自然科学基金资助项目(LY14E070001);浙江省公益技术应用研究计划基金资助项目(LGJ18F020001);浙江省公益技术应用研究计划基金资助项目(LGG18F010007)
- DOI：10.11959/j.issn.1000-436x.2018111
  中图分类号： TN911.73
- 网络出版日期：2018-07，
  
  纸质出版日期：2018-07-25
- 稿件说明：
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王金铭, 叶时平, 尉理哲, 等. 半张量积压缩感知模型的快速重构方法[J]. 通信学报, 2018,39(7):26-38.

Jinming WANG, Shiping YE, Lizhe YU, et al. Fast reconstruction method for compressed sensing model with semi-tensor product[J]. Journal on communications, 2018, 39(7): 26-38.
王金铭, 叶时平, 尉理哲, 等. 半张量积压缩感知模型的快速重构方法[J]. 通信学报, 2018,39(7):26-38. DOI： 10.11959/j.issn.1000-436x.2018111.

Jinming WANG, Shiping YE, Lizhe YU, et al. Fast reconstruction method for compressed sensing model with semi-tensor product[J]. Journal on communications, 2018, 39(7): 26-38. DOI： 10.11959/j.issn.1000-436x.2018111.

摘要

为降低随机观测矩阵在压缩感知应用中所需的存储空间，提升大尺寸图像重构的实时性，提出一种半张量积压缩感知方法。利用该方法构建低阶随机观测矩阵，对原始信号进行全局采样，随后将测量值进行分组处理并采用l

-范数（0＆lt;q＆lt;1）迭代重加权方法进行重构。与传统压缩感知方法相比，所提方法既可成倍减小随机观测矩阵所需的存储空间，又可在保证图像重构质量的前提下，大大提升重构速度。验证实验利用了几种不同大小的随机观测矩阵对2维灰度图像进行了测试，比较其重构图像的峰值信噪比

和重构时间。测试结果表明，利用所提方法在保证重构精度的前提下，可大大减小随机观测矩阵所需的存储空间（当降低为传统方法的

时，仍可得到与传统方法一致的重构质量），同时极大地提升重构的实时性，对于1024像素×1024像素大小的图像，其重构时间可提升近260倍。

Abstract

To reduce the storage space of random measurement matrix and improve the reconstruction efficiency for compressed sensing (CS)

a new sampling approach for CS with semi-tensor product (STP-CS) was proposed.The proposed approach generated a low dimensional random measurement matrix to sample the sparse signals.Then the solutions of the sparse vector were estimated group by group with a l

-minimization (0＆lt;q＆lt;1) iteratively re-weighted least-squares (IRLS) algorithm.Compared with traditional compressed sensing methods

the proposed approach outperformed conventional CS in speed of reconstruction and that it also obtained comparable quality in the reconstruction.Numerical experiments were conducted using gray-scale images

the peak signal-to-noise ratio (PSNR) and the reconstruction time of the reconstruction images were compared with the random matrices with different dimensions.Comparisons were also conducted with other low storage techniques.Numerical experiment results show that the STP-CS can effectively reduce the storage space of the random measurement matrix to

and decrease tow orders of magnitude of time that for conventional CS

while maintaining the reconstruction quality.Numerical results also show that the reconstruction time can be effectively improved 260 for the image size of 1 024×1 024.

关键词

Keywords

references

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