scholarly journals Overview of Compressed Sensing: Sensing Model, Reconstruction Algorithm, and Its Applications

2020 ◽  
Vol 10 (17) ◽  
pp. 5909
Author(s):  
Lixiang Li ◽  
Yuan Fang ◽  
Liwei Liu ◽  
Haipeng Peng ◽  
Jürgen Kurths ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Reconstruction Algorithm ◽  
Transmission Efficiency ◽  
Sampling Theorem ◽  
Reconstruction Algorithms ◽  
Intelligent Networks ◽  
Shannon Sampling Theorem ◽  
Sensing Model ◽  
Block Compressed Sensing ◽  
The Internet Of Things

With the development of intelligent networks such as the Internet of Things, network scales are becoming increasingly larger, and network environments increasingly complex, which brings a great challenge to network communication. The issues of energy-saving, transmission efficiency, and security were gradually highlighted. Compressed sensing (CS) helps to simultaneously solve those three problems in the communication of intelligent networks. In CS, fewer samples are required to reconstruct sparse or compressible signals, which breaks the restrict condition of a traditional Nyquist–Shannon sampling theorem. Here, we give an overview of recent CS studies, along the issues of sensing models, reconstruction algorithms, and their applications. First, we introduce several common sensing methods for CS, like sparse dictionary sensing, block-compressed sensing, and chaotic compressed sensing. We also present several state-of-the-art reconstruction algorithms of CS, including the convex optimization, greedy, and Bayesian algorithms. Lastly, we offer recommendation for broad CS applications, such as data compression, image processing, cryptography, and the reconstruction of complex networks. We discuss works related to CS technology and some CS essentials.

Ultrasonic Block Compressed Sensing Imaging Reconstruction Algorithm Based on Wavelet Sparse Representation

2020 ◽  
Vol 16 (3) ◽  
pp. 262-272
Author(s):  
Guangzhi Dai ◽  
Zhiyong He ◽  
Hongwei Sun
Keyword(s):  
Compressed Sensing ◽  
Sparse Representation ◽  
Linear Array ◽  
Imaging System ◽  
Ultrasonic Imaging ◽  
Large Data ◽  
Reconstruction Algorithm ◽  
Array Transducer ◽  
Total Data ◽  
Block Compressed Sensing

Background: This study is carried out targeting the problem of slow response time and performance degradation of imaging system caused by large data of medical ultrasonic imaging. In view of the advantages of CS, it is applied to medical ultrasonic imaging to solve the above problems. Objective: Under the condition of satisfying the speed of ultrasound imaging, the quality of imaging can be further improved to provide the basis for accurate medical diagnosis. Methods: According to CS theory and the characteristics of the array ultrasonic imaging system, block compressed sensing ultrasonic imaging algorithm is proposed based on wavelet sparse representation. Results: Three kinds of observation matrices have been designed on the basis of the proposed algorithm, which can be selected to reduce the number of the linear array channels and the complexity of the ultrasonic imaging system to some extent. Conclusion: The corresponding simulation program is designed, and the result shows that this algorithm can greatly reduce the total data amount required by imaging and the number of data channels required for linear array transducer to receive data. The imaging effect has been greatly improved compared with that of the spatial frequency domain sparse algorithm.

scholarly journals A New Regularized Reconstruction Algorithm Based on Compressed Sensing for the Sparse Underdetermined Problem and Applications of One-Dimensional and Two-Dimensional Signal Recovery

Algorithms ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 126 ◽  
Author(s):  
Bin Wang ◽  
Li Wang ◽  
Hao Yu ◽  
Fengming Xin
Keyword(s):  
Compressed Sensing ◽  
Reconstruction Algorithm ◽  
Steepest Descent Method ◽  
Signal Recovery ◽  
Two Dimensional ◽  
Reconstruction Algorithms ◽  
Experimental Conditions ◽  
One Dimensional ◽  
Recovery Algorithm ◽  
Reconstruction Performance

The compressed sensing theory has been widely used in solving undetermined equations in various fields and has made remarkable achievements. The regularized smooth L0 (ReSL0) reconstruction algorithm adds an error regularization term to the smooth L0(SL0) algorithm, achieving the reconstruction of the signal well in the presence of noise. However, the ReSL0 reconstruction algorithm still has some flaws. It still chooses the original optimization method of SL0 and the Gauss approximation function, but this method has the problem of a sawtooth effect in the later optimization stage, and the convergence effect is not ideal. Therefore, we make two adjustments to the basis of the ReSL0 reconstruction algorithm: firstly, we introduce another CIPF function which has a better approximation effect than Gauss function; secondly, we combine the steepest descent method and Newton method in terms of the algorithm optimization. Then, a novel regularized recovery algorithm named combined regularized smooth L0 (CReSL0) is proposed. Under the same experimental conditions, the CReSL0 algorithm is compared with other popular reconstruction algorithms. Overall, the CReSL0 algorithm achieves excellent reconstruction performance in terms of the peak signal-to-noise ratio (PSNR) and run-time for both a one-dimensional Gauss signal and two-dimensional image reconstruction tasks.

scholarly journals WSNs Compressed Sensing Signal Reconstruction Based on Improved Kernel Fuzzy Clustering and Discrete Differential Evolution Algorithm

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Zhou-zhou Liu ◽  
Shi-ning Li
Keyword(s):  
Compressed Sensing ◽  
Differential Evolution ◽  
Fuzzy Clustering ◽  
Clustering Algorithm ◽  
Signal Reconstruction ◽  
Differential Evolution Algorithm ◽  
Reconstruction Algorithm ◽  
Reconstruction Algorithms ◽  
Evolution Algorithm ◽  
Discrete Differential Evolution

To reconstruct compressed sensing (CS) signal fast and accurately, this paper proposes an improved discrete differential evolution (IDDE) algorithm based on fuzzy clustering for CS reconstruction. Aiming to overcome the shortcomings of traditional CS reconstruction algorithm, such as heavy dependence on sparsity and low precision of reconstruction, a discrete differential evolution (DDE) algorithm based on improved kernel fuzzy clustering is designed. In this algorithm, fuzzy clustering algorithm is used to analyze the evolutionary population, which improves the pertinence and scientificity of population learning evolution while realizing effective clustering. The differential evolutionary particle coding method and evolutionary mechanism are redefined. And the improved fuzzy clustering discrete differential evolution algorithm is applied to CS reconstruction algorithm, in which signal with unknown sparsity is considered as particle coding. Then the wireless sensor networks (WSNs) sparse signal is accurately reconstructed through the iterative evolution of population. Finally, simulations are carried out in the WSNs data acquisition environment. Results show that compared with traditional reconstruction algorithms such as StOMP, the reconstruction accuracy of the algorithm proposed in this paper is improved by 36.4-51.9%, and the reconstruction time is reduced by 15.1-31.3%.

scholarly journals Compressed sensing for electrocardiogram acquisition in wireless body sensor network: A comparative analysis

2019 ◽  
Vol 15 (7) ◽  
pp. 155014771986488 ◽  
Author(s):  
Junxin Chen ◽  
Jiazhu Xing ◽  
Leo Yu Zhang ◽  
Lin Qi
Keyword(s):  
Compressed Sensing ◽  
Sensor Network ◽  
Low Cost ◽  
Reconstruction Algorithm ◽  
Signal Acquisition ◽  
Reconstruction Algorithms ◽  
Practical Applications ◽  
Body Sensor Network ◽  
The Past ◽  
Electrocardiogram Signals

In the past decades, compressed sensing emerges as a promising technique for signal acquisition in low-cost sensor networks. For prolonging the monitoring duration of biosignals, compressed sensing is also exploited for simultaneous sampling and compression of electrocardiogram signals in the wireless body sensor network. This article presents a comprehensive analysis of compressed sensing for electrocardiogram acquisition. The performances of involved important factors, such as wavelet basis, overcomplete dictionaries, and the reconstruction algorithms, are comparatively illustrated, with the purpose to give data reference for practical applications. Drawn from a bulk of comparative experiments, the potential of compressed sensing in electrocardiogram acquisition is evaluated in different compression levels, while preferred sparsifying basis and reconstruction algorithm are also suggested. Relative perspectives and discussions are also given.

scholarly journals Energy Preserved Sampling for Compressed Sensing MRI

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yudong Zhang ◽  
Bradley S. Peterson ◽  
Genlin Ji ◽  
Zhengchao Dong
Keyword(s):  
Compressed Sensing ◽  
Cost Function ◽  
Computation Time ◽  
Reconstruction Algorithm ◽  
Simple Random Sampling ◽  
Variable Density ◽  
Reconstruction Algorithms ◽  
Iterative Thresholding ◽  
Thresholding Algorithm

The sampling patterns, cost functions, and reconstruction algorithms play important roles in optimizing compressed sensing magnetic resonance imaging (CS-MRI). Simple random sampling patterns did not take into account the energy distribution ink-space and resulted in suboptimal reconstruction of MR images. Therefore, a variety of variable density (VD) based samplings patterns had been developed. To further improve it, we propose a novel energy preserving sampling (ePRESS) method. Besides, we improve the cost function by introducing phase correction and region of support matrix, and we propose iterative thresholding algorithm (ITA) to solve the improved cost function. We evaluate the proposed ePRESS sampling method, improved cost function, and ITA reconstruction algorithm by 2D digital phantom and 2Din vivoMR brains of healthy volunteers. These assessments demonstrate that the proposed ePRESS method performs better than VD, POWER, and BKO; the improved cost function can achieve better reconstruction quality than conventional cost function; and the ITA is faster than SISTA and is competitive with FISTA in terms of computation time.

Modified meta-heuristic-oriented compressed sensing reconstruction algorithm for bio-signals

2019 ◽  
Vol 17 (05) ◽  
pp. 1950031
Author(s):  
Ashok Naganath Shinde ◽  
Sanjay L. Lalbalwar ◽  
Anil B. Nandgaonkar
Keyword(s):  
Compressed Sensing ◽  
Signal Reconstruction ◽  
Sampling Rate ◽  
Reconstruction Algorithm ◽  
Haar Wavelet ◽  
Evaluation Procedure ◽  
Grey Wolf Optimizer ◽  
Reconstruction Algorithms ◽  
Swarm Optimization ◽  
Glowworm Swarm Optimization

In signal processing, several applications necessitate the efficient reprocessing and representation of data. Compression is the standard approach that is used for effectively representing the signal. In modern era, many new techniques are developed for compression at the sensing level. Compressed sensing (CS) is a rising domain that is on the basis of disclosure, which is a little gathering of a sparse signal’s linear projections including adequate information for reconstruction. The sampling of the signal is permitted by the CS at a rate underneath the Nyquist sampling rate while relying on the sparsity of the signals. Additionally, the reconstruction of the original signal from some compressive measurements can be authentically exploited using the varied reconstruction algorithms of CS. This paper intends to exploit a new compressive sensing algorithm for reconstructing the signal in bio-medical data. For this purpose, the signal can be compressed by undergoing three stages: designing of stable measurement matrix, signal compression and signal reconstruction. In this, the compression stage includes a new working model that precedes three operations. They are signal transformation, evaluation of [Formula: see text] and normalization. In order to evaluate the theta ([Formula: see text]) value, this paper uses the Haar wavelet matrix function. Further, this paper ensures the betterment of the proposed work by influencing the optimization concept with the evaluation procedure. The vector coefficient of Haar wavelet function is optimally selected using a new optimization algorithm called Average Fitness-based Glowworm Swarm Optimization (AF-GSO) algorithm. Finally, the performance of the proposed model is compared over the traditional methods like Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), Firefly (FF), Crow Search (CS) and Glowworm Swarm Optimization (GSO) algorithms.

Wideband LFM Signal Parameter Estimation Based on Compressed Sensing Theory

2014 ◽  
Vol 548-549 ◽  
pp. 1160-1165 ◽  
Author(s):  
Ning Ma ◽  
Jian Xin Wang
Keyword(s):  
Parameter Estimation ◽  
Compressed Sensing ◽  
Sampling Theorem ◽  
Signal Spectrum ◽  
Reconstruction Algorithms ◽  
Edge Information ◽  
Compressed Sampling ◽  
Novel Method ◽  
Estimation Precision ◽  
Sampling And Reconstruction

Compressed sensing (CS) theory breaks through the limitations of the traditional Nyquist sampling theorem, and accomplishes the compressed sampling and reconstruction of signals based on sparsity or compressibility. In this paper, CS theory is used to do the parameter estimation of wideband Linear Frequency Modulated (LFM) signal in order to decrease the sampling pressure. A novel method that reconstructs the edge information of the LFM spectrum based on wavelet transform and CS theory is proposed. On the basis that the wideband LFM signal has approximate rectangular spectrum, the wavelet-based edge detection is introduced to provide sparse representation for the signal spectrum. The edges of the spectrum can be reconstructed by the CS reconstruction algorithms. Consequently, the initial frequency and final frequency of wideband LFM signal can be estimated with high estimation precision. The effectiveness of the proposed method is confirmed with numerical simulation.

scholarly journals Adaptive Reconstruction Algorithm Based on Compressed Sensing Broadband Receiver

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Wei-Jian Si ◽  
Qiang Liu ◽  
Zhi-An Deng
Keyword(s):  
Compressed Sensing ◽  
Signal To Noise Ratio ◽  
Adaptive Algorithms ◽  
Reconstruction Algorithm ◽  
Position Estimation ◽  
Accurate Estimation ◽  
Blind Estimation ◽  
Reconstruction Algorithms ◽  
Receiver System ◽  
Adaptive Reconstruction

Existing greedy reconstruction algorithms require signal sparsity, and the remaining sparsity adaptive algorithms can be reconstructed but cannot achieve accurate sparsity estimation. To address this problem, a blind sparsity reconstruction algorithm is proposed in this paper, which is applied to compressed sensing radar receiver system. The proposed algorithm can realize the estimation of signal sparsity and channel position estimation, which mainly consists of two parts. The first part is to use fast search based on dichotomy search, which is based on the high probability reconstruction of greedy algorithm, and uses dichotomy search to cover the number of sparsity. The second part is the signal matching and tracking algorithm, which is mainly used to judge the signal position and reconstruct the signal. Combine the two parts together to realize the blind estimation of the sparsity and the accurate estimation of the number of signals when the number of signals is unknown. The experimental analyses are carried out to evaluate the performance of the reconstruction probability, the accuracy of sparsity estimation, the running time of the algorithm, and the signal-to-noise ratio.

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