Noise Folding in Completely Perturbed Compressed Sensing

Journal of Applied Mathematics ◽

10.1155/2016/5094239 ◽

2016 ◽

Vol 2016 ◽

pp. 1-13

Author(s):

Limin Zhou ◽

Xinxin Niu ◽

Jing Yuan

Keyword(s):

Numerical Simulation ◽

Compressed Sensing ◽

Restricted Isometry Property ◽

Measurement Noise ◽

Original Signal ◽

Sensing Matrix ◽

Signal Noise ◽

Noise Folding

This paper first presents a new generally perturbed compressed sensing (CS) modely=(A+E)(x+u)+e, which incorporated a general nonzero perturbationEinto sensing matrixAand a noiseuinto signalxsimultaneously based on the standard CS modely=Ax+eand is called noise folding in completely perturbed CS model. Our construction mainly will whiten the new proposed CS model and explore in restricted isometry property (RIP) and coherence of the new CS model under some conditions. Finally, we use OMP to give a numerical simulation which shows that our model is feasible although the recovered value of signal is not exact compared with original signal because of measurement noisee, signal noiseu, and perturbationEinvolved.

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A Method of Reweighting the Sensing Matrix for Compressed Sensing

IEEE Access ◽

10.1109/access.2021.3054807 ◽

2021 ◽

Vol 9 ◽

pp. 21425-21432

Author(s):

Lei Shi ◽

Gangrong Qu ◽

Qian Wang

Keyword(s):

Compressed Sensing ◽

Sensing Matrix

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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.

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A Novel Coherence Reduction Method in Compressed Sensing for DOA Estimation

Journal of Applied Mathematics ◽

10.1155/2013/548979 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9

Author(s):

Jing Liu ◽

ChongZhao Han ◽

XiangHua Yao ◽

Feng Lian

Keyword(s):

Compressed Sensing ◽

Phased Array ◽

Reduction Method ◽

Doa Estimation ◽

Estimation Methods ◽

Sensing Matrix ◽

Replacement Method ◽

Precise Estimation ◽

Novel Method ◽

Measurement Vector

A novel method named as coherent column replacement method is proposed to reduce the coherence of a partially deterministic sensing matrix, which is comprised of highly coherent columns and random Gaussian columns. The proposed method is to replace the highly coherent columns with random Gaussian columns to obtain a new sensing matrix. The measurement vector is changed accordingly. It is proved that the original sparse signal could be reconstructed well from the newly changed measurement vector based on the new sensing matrix with large probability. This method is then extended to a more practical condition when highly coherent columns and incoherent columns are considered, for example, the direction of arrival (DOA) estimation problem in phased array radar system using compressed sensing. Numerical simulations show that the proposed method succeeds in identifying multiple targets in a sparse radar scene, where the compressed sensing method based on the original sensing matrix fails. The proposed method also obtains more precise estimation of DOA using one snapshot compared with the traditional estimation methods such as Capon, APES, and GLRT, based on hundreds of snapshots.

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