Beyond The Sampling Theorem- Compressive Sensing and its Applications

Compressive sensing has the ability of reconstruction of signal/image from the compressive measurements which are sensed with a much lower number of samples than a minimum requirement by Nyquist sampling theorem. The random acquisition is widely suggested and used for compressive sensing. In the random acquisition, the randomness of the sparsity structure has been deployed for compressive sampling of the signal/image. The article goes through all the literature up to date and collects the main methods, and simply described the way each of them randomly applies the compressive sensing. This article is a comprehensive review of random acquisition techniques in compressive sensing. Theses techniques have reviews under the main categories of (1) random demodulator, (2) random convolution, (3) modulated wideband converter model, (4) compressive multiplexer diagram, (5) random equivalent sampling, (6) random modulation pre-integration, (7) quadrature analog-to-information converter, (8) randomly triggered modulated-wideband compressive sensing (RT-MWCS).

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Compressive Sensing Based Channel Estimation for Massive MIMO Communication Systems

Wireless Communications and Mobile Computing ◽

10.1155/2019/6374764 ◽

2019 ◽

Vol 2019 ◽

pp. 1-15 ◽

Cited By ~ 3

Author(s):

Athar Waseem ◽

Aqdas Naveed ◽

Sardar Ali ◽

Muhammad Arshad ◽

Haris Anis ◽

...

Keyword(s):

Channel Estimation ◽

Compressive Sensing ◽

Massive Mimo ◽

Communication Systems ◽

Mimo Systems ◽

Multiple Input Multiple Output ◽

Sampling Theorem ◽

Base Station ◽

Mimo Channels ◽

Pilot Design

Massive multiple-input multiple-output (MIMO) is believed to be a key technology to get 1000x data rates in wireless communication systems. Massive MIMO occupies a large number of antennas at the base station (BS) to serve multiple users at the same time. It has appeared as a promising technique to realize high-throughput green wireless communications. Massive MIMO exploits the higher degree of spatial freedom, to extensively improve the capacity and energy efficiency of the system. Thus, massive MIMO systems have been broadly accepted as an important enabling technology for 5th Generation (5G) systems. In massive MIMO systems, a precise acquisition of the channel state information (CSI) is needed for beamforming, signal detection, resource allocation, etc. Yet, having large antennas at the BS, users have to estimate channels linked with hundreds of transmit antennas. Consequently, pilot overhead gets prohibitively high. Hence, realizing the correct channel estimation with the reasonable pilot overhead has become a challenging issue, particularly for frequency division duplex (FDD) in massive MIMO systems. In this paper, by taking advantage of spatial and temporal common sparsity of massive MIMO channels in delay domain, nonorthogonal pilot design and channel estimation schemes are proposed under the frame work of structured compressive sensing (SCS) theory that considerably reduces the pilot overheads for massive MIMO FDD systems. The proposed pilot design is fundamentally different from conventional orthogonal pilot designs based on Nyquist sampling theorem. Finally, simulations have been performed to verify the performance of the proposed schemes. Compared to its conventional counterparts with fewer pilots overhead, the proposed schemes improve the performance of the system.

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Cylindrical Three-Dimensional Millimeter-Wave Imaging via Compressive Sensing

International Journal of Antennas and Propagation ◽

10.1155/2015/218751 ◽

2015 ◽

Vol 2015 ◽

pp. 1-6 ◽

Cited By ~ 3

Author(s):

Guoqiang Zhao ◽

Shiyong Li ◽

Bailing Ren ◽

Qingwei Qiu ◽

Houjun Sun

Keyword(s):

Compressive Sensing ◽

Millimeter Wave ◽

Imaging Techniques ◽

New Technology ◽

Three Dimensional ◽

Sampling Theorem ◽

Future Application ◽

Imaging Method ◽

Wave Imaging ◽

The Cost

Millimeter-wave (MMW) imaging techniques have been used for the detection of concealed weapons and contraband carried by personnel. However, the future application of the new technology may be limited by its large number of antennas. In order to reduce the complexity of the hardware, a novel MMW imaging method based on compressive sensing (CS) is proposed in this paper. The MMW images can be reconstructed from the significantly undersampled backscattered data via the CS approach. Thus the number of antennas and the cost of system can be further reduced than those based on the traditional imaging methods that obey the Nyquist sampling theorem. The effectiveness of the proposed method is validated by numerical simulations as well as by real measured data of objects.

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Analysis of the Effect of Noise in CosaMP Algorithm

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.926-930.2992 ◽

2014 ◽

Vol 926-930 ◽

pp. 2992-2995

Author(s):

Zheng Pu Zhang ◽

Xing Feng Guo ◽

Bo Tian

Keyword(s):

Signal Processing ◽

Compressive Sensing ◽

Digital Signal ◽

Sampling Theorem ◽

The Novel ◽

Reconstruction Algorithms ◽

Research Directions ◽

Comparison Results ◽

New Type ◽

The Given

Compressive sensing is a new type of digital signal processing method. The novel objective of compressive Sensing is to reconstruct a signal accurately and efficiently from far fewer sampling points got by Nyquist sampling theorem. Compressive sensing theory combines the process of sampling and compression to reduce the complexity of signal processing, which is widely used in many fields. so there are wide application prospects in the areas of radar image, wireless sensor network (WSN), radio frequency communication, medical image processing, image device collecting and so on. One of the important tasks in CS is how to recover the signals more accurately and effectively, which is concerned by many researchers. Compressive sensing started late; there are many problems and research directions worthy of our in-depth research. At present, many researchers shove focused on reconstruction algorithms. Reconstruction algorithms are the core of compressive sensing, which are of great significance to reconstructing compressed signals and verifying the accuracy in sampling. These papers introduce CosaMP algorithm; and then study and analyze the Gaussian noise as the main content. Finally, the given signal and random signal, for example, we give a series of comparison results.

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An MCM-Enhanced Compressive Sensing for Weak Fault Feature Extraction of Rolling Element Bearings under Variable Speeds

Shock and Vibration ◽

10.1155/2020/1745184 ◽

2020 ◽

Vol 2020 ◽

pp. 1-21

Author(s):

Ya He ◽

Kun Feng ◽

Minghui Hu ◽

Jinmiao Cui

Keyword(s):

Compressive Sensing ◽

Circulant Matrix ◽

Sampling Theorem ◽

Rolling Element Bearings ◽

Measurement Matrix ◽

Rolling Bearings ◽

Time Frequency ◽

Rolling Element ◽

Shannon Sampling Theorem ◽

Weak Fault

The compressive sensing (CS) theory provides a new slight to the big-data problem led by the Shannon sampling theorem in rolling element bearings condition monitoring, where the measurement matrix of CS tends to be designed by the random matrix (RM) to preserve the integrity of signal roughly. However, when the signal to be analyzed is infected with strong noise, not only does the signal become insufficiently sparse, but the randomness of the measurement matrix will bring down the sensing efficiency, resulting in the loss of fault feature. Thus, a sensing-enhanced CS scheme based on a series of modes after VMD decomposition is proposed under this paper. The core of this scheme is as follows: (1) the principal mode of VMD with better sparsity replaces the raw signal for compressive sensing; (2) all these modes contain the time-frequency characteristics of the raw signal; (3) a new measurement matrix called mode-circulant matrix (MCM) is defined by circulating the mode matrix, and when the amount of samples is shrunk, the sensing efficiency can be enhanced greatly. Besides, considering the fault signal of rolling bearings under variable speed, there is a need to use order tracking to overcome the nonstationarity of the signal before applying CS theory. The analysis results of simulation and experiment prove that the VMD- and MCM-based CS can successfully extract the weak fault feature of rolling bearings with operating speed changing.

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Study and Discussion on the Theory of Compressive Sensing

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.239-240.1462 ◽

2012 ◽

Vol 239-240 ◽

pp. 1462-1465

Author(s):

Ying Zhu ◽

Yong Xing Jia ◽

Yuan Wang

Keyword(s):

Information Theory ◽

Compressive Sensing ◽

Sparse Representation ◽

Hardware Implementation ◽

Sampling Theorem ◽

Sampling Frequency ◽

Main Process ◽

Follow Up Studies

Compressive sensing(CS)is a novel information theory proposed recently.It broke through the restrictions of the traditional Nyquist sampling theorem on the sampling frequency,which can only use fewer sampling signals to describe the original signals. This article introduces the theory of CS including three main process like sparse representation, mesurement matric design and signal reconstruction.Then it also discusses the issures requiring improvement about the algorithm,the hardware implementation ,finds the reasons and gives some advices in follow-up studies.

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Noises in randomly sampled sparse signals

Facta universitatis - series Electronics and Energetics ◽

10.2298/fuee1403359s ◽

2014 ◽

Vol 27 (3) ◽

pp. 359-373 ◽

Cited By ~ 1

Author(s):

Ljubisa Stankovic

Keyword(s):

Compressive Sensing ◽

Random Sampling ◽

Domain Analysis ◽

External Noise ◽

Sampling Theorem ◽

Sparse Signals ◽

Gradient Based

Sparse signals can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Two main reconstruction directions are in the sparse transformation domain analysis of signals and the gradient based algorithms. In the transformation domain analysis, that will be considered here, the estimation of nonzero signal coefficients is based on the signal transform calculated using available samples only. The missing samples manifest themselves as a noise. This kind of noise is analyzed in the case of random sampling, when the sampling instants do not coincide with the sampling theorem instants. Analysis of the external noise influence to the results, with randomly sampled sparse signals, is done as well. Theory is illustrated and checked on statistical examples.

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ON TIKHONOV REGULARIZATION AND COMPRESSIVE SENSING FOR SEISMIC SIGNAL PROCESSING

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202511500084 ◽

2012 ◽

Vol 22 (02) ◽

pp. 1150008 ◽

Cited By ~ 10

Author(s):

YANFEI WANG ◽

CHANGCHUN YANG ◽

JINGJIE CAO

Keyword(s):

Compressive Sensing ◽

Tikhonov Regularization ◽

Signal Reconstruction ◽

Gradient Methods ◽

Seismic Signal ◽

Sampling Theorem ◽

Sparse Regularization ◽

Reflection Seismic ◽

Reconstruction Methods ◽

Ill Posed

Using compressive sensing and sparse regularization, one can nearly completely reconstruct the input (sparse) signal using limited numbers of observations. At the same time, the reconstruction methods by compressing sensing and optimizing techniques overcome the obstacle of the number of sampling requirement of the Shannon/Nyquist sampling theorem. It is well known that seismic reflection signal may be sparse, sometimes and the number of sampling is insufficient for seismic surveys. So, the seismic signal reconstruction problem is ill-posed. Considering the ill-posed nature and the sparsity of seismic inverse problems, we study reconstruction of the wavefield and the reflection seismic signal by Tikhonov regularization and the compressive sensing. The l0, l1 and l2 regularization models are studied. Relationship between Tikhonov regularization and the compressive sensing is established. In particular, we introduce a general lp - lq (p, q ≥ 0) regularization model, which overcome the limitation on the assumption of convexity of the objective function. Interior point methods and projected gradient methods are studied. To show the potential for application of the regularized compressive sensing method, we perform both synthetic seismic signal and field data compression and restoration simulations using a proposed piecewise random sub-sampling. Numerical performance indicates that regularized compressive sensing is applicable for practical seismic imaging.

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Compressed Sensing Speech Signal Enhancement Research

Indonesian Journal of Electrical Engineering and Computer Science ◽

10.11591/ijeecs.v6.i1.pp26-35 ◽

2017 ◽

Vol 6 (1) ◽

pp. 26

Author(s):

Kuangfeng Ning ◽

Guojun Qin

Keyword(s):

Compressed Sensing ◽

Compressive Sensing ◽

Input Signal ◽

Speech Signal ◽

Signal To Noise Ratio ◽

Sampling Theorem ◽

Compressed Domain ◽

Signal To Noise ◽

Perceptual Evaluation

The proposed Compressive sensing method is a new alternative method, it is used to eliminate noise from the input signal, and the quality of the speech signal is enhanced with fewer samples, thus it is required for the reconstruction than needed in some of the methods like Nyquist sampling theorem. The basic idea is that the speech signals are sparse in nature, and most of the noise signals are non-sparse in nature, and Compressive Sensing(CS) eliminates the non-sparse components and it reconstructs only the sparse components of the input signal. Experimental results prove that the average segmental SNR (signal to noise ratio) and PESQ (perceptual evaluation of speech quality) scores are better in the compressed domain．

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Compressive Sensing for Wireless Networks

10.1017/cbo9781139088497 ◽

2009 ◽

Cited By ~ 51

Author(s):

Zhu Han ◽

Husheng Li ◽

Wotao Yin

Keyword(s):

Wireless Networks ◽

Compressive Sensing

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