Learning‐based design of random measurement matrix for compressed sensing with inter‐column correlation using copula function

Compressed Sensing(CS) can project a high dimensional signal to a low dimensional signal by a random measurement matrix . As the projection calculation is time-consuming in the process of reconstruction, the reconstruction speed is greatly affected.In order to improve the reconstruction speed , some improvement in the selection of the measurement matrix and the design of the reconstruction algorithm is made. The wavelet transform is used to sparse decompose the image, and the very sparse random projection matrix is used as the measurement matrix, after the image block processing we use the OMP algorithm to reconstruct the image. The experimental result shows that this method could reduce the algorithm time and improved the reconstruction speed greatly.

Download Full-text

Improvement of Semi-Random Measurement Matrix for Compressed Sensing

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

10.1587/transfun.e97.a.1426 ◽

2014 ◽

Vol E97.A (6) ◽

pp. 1426-1429 ◽

Cited By ~ 1

Author(s):

Wentao LV ◽

Junfeng WANG ◽

Wenxian YU ◽

Zhen TAN

Keyword(s):

Compressed Sensing ◽

Measurement Matrix ◽

Random Measurement

Download Full-text

A Note on Stability and Instance Optimality in Compressed Sensing

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.130-134.4194 ◽

2011 ◽

Vol 130-134 ◽

pp. 4194-4197

Author(s):

Sheng Zhang ◽

Pei Xin Ye

Keyword(s):

Compressed Sensing ◽

Noisy Data ◽

Sparse Signal ◽

Measurement Matrix ◽

Random Measurement ◽

Restricted Isometry Constant ◽

Instance Optimality ◽

Measurement Vector ◽

The Stability ◽

Signal Vector

In this note, it is proved that every -sparse signal vector can be recovered stably from the measurement vector via minimization as soon as the restricted isometry constant of the measurement matrix is smaller than . Note that our results contain the case of noisy data, therefore previous known results in the literature are extent and improved. Also we obtain the results on the stability and instance optimality for some random measurement matrices.

Download Full-text

Restricted isometry constant improvement based on a singular value decomposition-weighted measurement matrix for compressed sensing

IET Communications ◽

10.1049/iet-com.2016.1435 ◽

2017 ◽

Vol 11 (11) ◽

pp. 1706-1718 ◽

Cited By ~ 4

Author(s):

Qian Wang ◽

Gangrong Qu

Keyword(s):

Singular Value Decomposition ◽

Compressed Sensing ◽

Singular Value ◽

Measurement Matrix ◽

Restricted Isometry Constant ◽

Value Decomposition ◽

Constant Improvement

Download Full-text

Compressed Sampling of Spectrally Sparse Signals Using Sparse Circulant Matrices

Frequenz ◽

10.1515/freq-2014-0036 ◽

2014 ◽

Vol 68 (11-12) ◽

Cited By ~ 1

Author(s):

Guangjie Xu ◽

Huali Wang ◽

Lei Sun ◽

Weijun Zeng ◽

Qingguo Wang

Keyword(s):

Circulant Matrices ◽

Noise Robustness ◽

Sparse Signals ◽

Measurement Matrix ◽

Compressed Sampling ◽

Random Measurement ◽

Compressive Performance ◽

Generating Sequence ◽

Periodic Autocorrelation ◽

Selection Of

AbstractCirculant measurement matrices constructed by partial cyclically shifts of one generating sequence, are easier to be implemented in hardware than widely used random measurement matrices; however, the diminishment of randomness makes it more sensitive to signal noise. Selecting a deterministic sequence with optimal periodic autocorrelation property (PACP) as generating sequence, would enhance the noise robustness of circulant measurement matrix, but this kind of deterministic circulant matrices only exists in the fixed periodic length. Actually, the selection of generating sequence doesn't affect the compressive performance of circulant measurement matrix but the subspace energy in spectrally sparse signals. Sparse circulant matrices, whose generating sequence is a sparse sequence, could keep the energy balance of subspaces and have similar noise robustness to deterministic circulant matrices. In addition, sparse circulant matrices have no restriction on length and are more suitable for the compressed sampling of spectrally sparse signals at arbitrary dimensionality.

Download Full-text

Research on Compressed Sensing Matrix Based on Data Compressing of Insulator Leakage Current

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.475-476.451 ◽

2013 ◽

Vol 475-476 ◽

pp. 451-454

Author(s):

Xue Ming Zhai ◽

Xiao Bo You ◽

Ruo Chen Li ◽

Yu Jia Zhai ◽

De Wen Wang

Keyword(s):

Compressed Sensing ◽

Data Compression ◽

Leakage Current ◽

Sparse Matrix ◽

Circulant Matrix ◽

Measurement Matrix ◽

Sensing Matrix ◽

Significant Step ◽

On Line

Insulator fault may lead to the accident of power network,thus the on-line monitoring of insulator is very significant. Low rates wireless network is used for data transmission of leakage current. Making data compression and reconstruction of leakage current with the compressed sensing theory can achieve pretty good results. Determination of measurement matrix is the significant step for realizing the compressed sensing theory. This paper compares multiple measurement matrix of their effect via experiments, putting forward to make data compression and reconstruction of leakage current using Toeplitz matrix, circulant matrix and sparse matrix as measurement matrix, of which the reconstitution effect is almost the same as classical measurement matrix and depletes computational complexity and workload.

Download Full-text