scholarly journals A Method of Constructing Measurement Matrix for Compressed Sensing by Chebyshev Chaotic Sequence

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1085
Author(s):  
Renjie Yi ◽  
Chen Cui ◽  
Yingjie Miao ◽  
Biao Wu
Keyword(s):  
Compressed Sensing ◽  
High Probability ◽  
Hardware Implementation ◽  
Electric Circuit ◽  
Chaotic Sequence ◽  
Measurement Matrix ◽  
Chaotic Sequences ◽  
Reconstruction Performance ◽  
Simulation Results ◽  
Sample Distance

In this paper, the problem of constructing the measurement matrix in compressed sensing is addressed. In compressed sensing, constructing a measurement matrix of good performance and easy hardware implementation is of interest. It has been recently shown that the measurement matrices constructed by Logistic or Tent chaotic sequences satisfy the restricted isometric property (RIP) with a certain probability and are easy to be implemented in the physical electric circuit. However, a large sample distance that means large resources consumption is required to obtain uncorrelated samples from these sequences in the construction. To solve this problem, we propose a method of constructing the measurement matrix by the Chebyshev chaotic sequence. The method effectively reduces the sample distance and the proposed measurement matrix is proved to satisfy the RIP with high probability on the assumption that the sampled elements are statistically independent. Simulation results show that the proposed measurement matrix has comparable reconstruction performance to that of the existing chaotic matrices for compressed sensing.

A Randomly Permuted Fourier Measurement Matrix for UWB-PPM Signals

2014 ◽  
Vol 556-562 ◽  
pp. 2646-2649 ◽  
Author(s):  
Hai Bo Yin ◽  
Jun An Yang ◽  
Wei Dong Wang
Keyword(s):  
Compressed Sensing ◽  
Structural Features ◽  
Measurement Matrix ◽  
Reconstruction Accuracy ◽  
High Sampling ◽  
Reconstruction Performance ◽  
Simulation Results ◽  
Hardware Costs ◽  
Fourier Matrix

Compressed Sensing is likely to provide an effective way for lowering the extremely high sampling speed of UWB signal while the design of CS measurement matrix is of great significance for reducing the number of observations and hardware costs as long as improving the reconstruction accuracy. In this paper, with the combination of the structural features of the Fourier matrix and the idea of entry permutation of determined matrices, we propose a new measurement matrix of which the Fourier transformed entries are randomly permuted. Simulation results show that the same algorithm has a better reconstruction performance with the proposed measurement matrix rather than Gaussian/ Bernoulli matrix.

ADAPTIVE IDENTIFICATION ALGORITHMS FOR AR SYSTEM DRIVEN BY CHAOTIC SEQUENCE

2003 ◽  
Vol 13 (04) ◽  
pp. 963-972 ◽  
Author(s):  
BAO-YUN WANG ◽  
T. W. S. CHOW ◽  
K. T. NG
Keyword(s):  
Communication System ◽  
Adaptive Algorithms ◽  
Chaotic Sequence ◽  
Estimation Accuracy ◽  
Chaotic Communication ◽  
Adaptive Identification ◽  
System Parameters ◽  
Chaotic Sequences ◽  
Simulation Results ◽  
Typical Method

In this article the identification of AR system driven by chaotic sequences is addressed. This problem emerges in chaotic communication system, in which chaos-modulated signal passes through a channel described as an AR system. Two adaptive algorithms are presented to tackle this problem. Compared with the existing algorithms such as MPSV and MNPE, the proposed algorithms have very low computational complexities and can be used to track the system parameters in a slowly time-variant environment. The obtained simulation results illustrate that the proposed scheme can offer a better estimation accuracy than the conventional typical method in the high SNR case.

scholarly journals A Two-Step Compressed Sensing Approach for Single-Snapshot DOA Estimation of Closely Spaced Signals

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shuang Wei ◽  
Yanhua Long ◽  
Rui Liu ◽  
Ying Su
Keyword(s):  
Compressed Sensing ◽  
Doa Estimation ◽  
Estimation Methods ◽  
Estimation Accuracy ◽  
Accurate Estimation ◽  
Measurement Matrix ◽  
Chaotic Sequences ◽  
Overcomplete Dictionary ◽  
Highly Correlated ◽  
Single Snapshot

Single-snapshot direction-of-arrival (DOA) estimation plays an important role in dynamic target detection and tracking applications. Because a single-snapshot signal provides few information for statistics calculation, recently compressed sensing (CS) theory is applied to solve single-snapshot DOA estimation, instead of the traditional DOA methods based on statistics. However, when the unknown sources are closely located, the spatial signals are highly correlated, and its overcomplete dictionary is made up of dense grids, which leads to a serious decrease in the estimation accuracy of the CS-based algorithm. In order to solve this problem, this paper proposed a two-step compressed sensing-based algorithm for the single-snapshot DOA estimation of closely spaced signals. The overcomplete dictionaries with coarse and refined grids are used in the two steps, respectively. The measurement matrix is constructed by using a very sparse projection scheme based on chaotic sequences because chaotic sequences have determinism and pseudo-randomness property. Such measurement matrix is mainly proposed for compressing the overcomplete dictionary in preestimation step, while it is well designed by choosing the steering vectors of true DOA in the accurate estimation step, in which the neighborhood information around the true DOAs partly solved in the previous step will be used. Monte Carlo simulation results demonstrate that the proposed algorithm can perform better than other existing single-snapshot DOA estimation methods. Especially, it can work well to solve the issues caused by closely spaced signals and single snapshot.

scholarly journals Image Encryption Scheme with Compressed Sensing Based on a New Six-Dimensional Non-Degenerate Discrete Hyperchaotic System and Plaintext-Related Scrambling

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 291
Author(s):  
Chunyang Sun ◽  
Erfu Wang ◽  
Bing Zhao
Keyword(s):  
Compressed Sensing ◽  
Image Compression ◽  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Chaotic Map ◽  
Hyperchaotic System ◽  
Encryption Scheme ◽  
Measurement Matrix ◽  
Reconstruction Performance

Digital images can be large in size and contain sensitive information that needs protection. Compression using compressed sensing performs well, but the measurement matrix directly affects the signal compression and reconstruction performance. The good cryptographic characteristics of chaotic systems mean that using one to construct the measurement matrix has obvious advantages. However, existing low-dimensional chaotic systems have low complexity and generate sequences with poor randomness. Hence, a new six-dimensional non-degenerate discrete hyperchaotic system with six positive Lyapunov exponents is proposed in this paper. Using this chaotic system to design the measurement matrix can improve the performance of image compression and reconstruction. Because image encryption using compressed sensing cannot resist known- and chosen-plaintext attacks, the chaotic system proposed in this paper is introduced into the compressed sensing encryption framework. A scrambling algorithm and two-way diffusion algorithm for the plaintext are used to encrypt the measured value matrix. The security of the encryption system is further improved by generating the SHA-256 value of the original image to calculate the initial conditions of the chaotic map. A simulation and performance analysis shows that the proposed image compression-encryption scheme has high compression and reconstruction performance and the ability to resist known- and chosen-plaintext attacks.

scholarly journals Application of M Sequence Family Measurement Matrix in Streak Camera Imaging

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Ailin Liu ◽  
Jinjin Zhang ◽  
Baoping Guo
Keyword(s):  
Compressed Sensing ◽  
Imaging System ◽  
Streak Camera ◽  
Contrast Ratio ◽  
Central Area ◽  
Measurement Matrix ◽  
Camera Imaging ◽  
Reconstruction Performance ◽  
Imaging Results ◽  
Improvement Effect

This study investigates the reduction in the resolution of the striations from the center to the edge through analysis of the imaging principle and the static experimental test of a streak tube. To improve the edge spatial resolution of the streak, we apply the compressed sensing to the X-ray streak camera imaging system and construct the compressed sensing (CS) reconstruction model for the streak camera and we implement the CS objective function by the orthogonal matching method. The reconstruction performance of the Gauss measurement matrix, Bernoulli measurement matrix, and M series family measurement matrix are compared, and the reconstruction parameters are optimized. A comparison between the original imaging results and the reconstruction results shows that the contrast ratio of the CS reconstruction is 12.2% higher than that of the original, and the limit resolution is 5 lp/mm higher than that of the original image. Furthermore, the improvement effect far from the central area is better than that at the central area. The CS reconstruction on the M series family measurement matrix can improve the image contrast ratio on the edge of the image, and, thus, static and dynamic spatial resolutions of the image are improved.

Measurement Matrix Construction Based on Differential Evolution Algorithm

2014 ◽  
Vol 644-650 ◽  
pp. 1007-1010
Author(s):  
Hua Xu
Keyword(s):  
Compressed Sensing ◽  
Differential Evolution ◽  
Differential Evolution Algorithm ◽  
Optimization Procedure ◽  
Ldpc Code ◽  
Measurement Matrix ◽  
Reconstruction Performance ◽  
The Matrix ◽  
Novel Method ◽  
Matrix Construction

Measurement matrix construction is important to compressed sensing. A novel method, MMC-DE (Measurement Matrix Construction based on Differential Evolution), is proposed in this paper. The matrix is based on the quasi-cyclic Low-Density Parity-Check (LDPC) code. This proposed method aims at constructing the quasi-cyclic matrix with the best girth during the optimization procedure. It can consequently result in improving the reconstruction performance of the measurement matrix for compressed sensing. Simulation results demonstrate that the proposed measurement matrix is better than the matrix of Tanner code and array code. It is also easy to implement and hardware friendly.

scholarly journals A New Method of Measurement Matrix Optimization for Compressed Sensing Based on Alternating Minimization

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 329
Author(s):  
Renjie Yi ◽  
Chen Cui ◽  
Biao Wu ◽  
Yang Gong
Keyword(s):  
Compressed Sensing ◽  
New Method ◽  
Gram Matrix ◽  
Alternating Minimization ◽  
Measurement Matrix ◽  
Mutual Coherence ◽  
Matrix Optimization ◽  
Shrinkage Function ◽  
Reconstruction Performance ◽  
Method Of Measurement

In this paper, a new method of measurement matrix optimization for compressed sensing based on alternating minimization is introduced. The optimal measurement matrix is formulated in terms of minimizing the Frobenius norm of the difference between the Gram matrix of sensing matrix and the target one. The method considers the simultaneous minimization of the mutual coherence indexes including maximum mutual coherence μmax, t-averaged mutual coherence μave and global mutual coherence μall, and solves the problem that minimizing a single index usually results in the deterioration of the others. Firstly, the threshold of the shrinkage function is raised to be higher than the Welch bound and the relaxed Equiangular Tight Frame obtained by applying the new function to the Gram matrix is taken as the initial target Gram matrix, which reduces μave and solves the problem that μmax would be larger caused by the lower threshold in the known shrinkage function. Then a new target Gram matrix is obtained by sequentially applying rank reduction and eigenvalue averaging to the initial one, leading to lower. The analytical solutions of measurement matrix are derived by SVD and an alternating scheme is adopted in the method. Simulation results show that the proposed method simultaneously reduces the above three indexes and outperforms the known algorithms in terms of reconstruction performance.

scholarly journals Constrained Backtracking Matching Pursuit Algorithm for Image Reconstruction in Compressed Sensing

2021 ◽  
Vol 11 (4) ◽  
pp. 1435
Author(s):  
Xue Bi ◽  
Lu Leng ◽  
Cheonshik Kim ◽  
Xinwen Liu ◽  
Yajun Du ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Compressed Sensing ◽  
Matching Pursuit ◽  
Reconstruction Algorithm ◽  
Energy Criterion ◽  
Step Size ◽  
Relationship Analysis ◽  
Support Set ◽  
Reconstruction Performance ◽  
Sparsity Level

Image reconstruction based on sparse constraints is an important research topic in compressed sensing. Sparsity adaptive matching pursuit (SAMP) is a greedy pursuit reconstruction algorithm, which reconstructs signals without prior information of the sparsity level and potentially presents better reconstruction performance than other greedy pursuit algorithms. However, SAMP still suffers from being sensitive to the step size selection at high sub-sampling ratios. To solve this problem, this paper proposes a constrained backtracking matching pursuit (CBMP) algorithm for image reconstruction. The composite strategy, including two kinds of constraints, effectively controls the increment of the estimated sparsity level at different stages and accurately estimates the true support set of images. Based on the relationship analysis between the signal and measurement, an energy criterion is also proposed as a constraint. At the same time, the four-to-one rule is improved as an extra constraint. Comprehensive experimental results demonstrate that the proposed CBMP yields better performance and further stability than other greedy pursuit algorithms for image reconstruction.

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