Compressive Sampling Matching Pursuit Research Articles

Coherence-based sufficient condition for support recovery using block generalized orthogonal matching pursuit

Challenge is to find the support vectors of the unknown block sparse vector with compressed measurements in an underdetermined system where the number of unknowns is more than that of measurements. To recover unknown block sparse vector, restricted isometry property (RIP) is a sufficient condition need to be satisfied. Finding the restricted isometric constant is a non-polynomial hard problem for large values of n. In this paper coherence-based recovery guarantee has been proposed to recover the support vectors using block generalized orthogonal matching pursuit (BGOMP). It is proved that BGOMP can able to recover the support vectors with lesser number of iteration than block orthogonal matching pursuit (BOMP) by selecting multiple block support elements per iteration. Simulation results show detection performance of BGOMP is better than BOMP, block subspace pursuit (BSP) and block compressive sampling matching pursuit (BCoSaMP) for different block sparsity and block length. In most of the cases for different block sparsity and block length computation time for BGOMP is lesser than BCoSaMP, BSP and BOMP due to the multiple selection of elements in each iteration.

Supraharmonic Detection Algorithm Based on Interpolation of Self-Convolutional Window All-Phase Compressive Sampling Matching Pursuit

With the increase in the use of high-frequency power electronic devices, the harmonics injected into the power grid show a trend of high-frequency development. The continuous rise of the supraharmonic emission level in the distribution network has become one of the power quality problems that needs to be solved urgently in the power grid. In this paper, an algorithm based on the Interpolation of the Self-convolutional Window All-phase Compressive Sampling Matching Pursuit (ISWApCoSaMP) is proposed. Firstly, the self-convolution operation is used for the maximum sidelobe decay (MSD) window, and then the compressed sampling matching pursuit model based on the All-phase is constructed, leading to the All-phase Compressive Sampling Matching Pursuit (ApCoSaMP). Finally, the four-spectrum-line interpolation is combined to utilize spectrum line information to improve the accuracy of signal parameter detection in the frequency domain. The introduced All-phase greatly improves the phase measurement accuracy because the initial phase of the supraharmonic signal is selected for phase estimation. In addition, the self-convolutional window and four-spectrum-line interpolation make full use of the information in the time and frequency domains, thus optimizing the measurement results of amplitude and frequency. The algorithm achieves high accuracy in the measurement results of simulated signals and accurately measures supraharmonics.

Channel estimation and MIMO combining architecture in millimeter wave cellular system with few ADC bits

Hybrid combiner and precoder architectures, radio frequency (RF) chain, analog phase shifters, digital-to-analog converter (DAC), and analog-to-digital converter (ADC) are components of a millimeter wave cellular system. Prior works in the area of millimeter wave cellular system design employ receiver with infinite bit and large amount of RF chain that scales linearly with the quantity of transmitting and receiving antennas. This mode of design no doubt increases power demand or requirement of a typical millimeter wave system. In this work, hybrid architecture with few RF chains and small number of ADC bits are proposed and are used as candidate for millimeter wave channel estimation and cellular communication. In that connection, least square (LS), orthogonal matching pursuit (OMP), compressed sampling matching pursuit (CoSAMP), and deep learning (DL) techniques are utilized for analytical investigation. Indeed, computational results reveal that, when ADC consisting of uniform mid- rise quantizer is employed, the performance of 4 and 6 bits at signal-to-noise ratio (SNR) values of − 10 dB and 20 dB is at par with infinite bit (unquantized case). As a validation, DL compares favorably well with adaptive compressed sensing (ACS) technique previously used in the literature for channel estimation, while OMP and CoSAMP show better performance than ACS.

Image reconstruction through compressive sampling matching pursuit and curvelet transform

An interesting area of research is image reconstruction, which uses algorithms and techniques to transform a degraded image into a good one. The quality of the reconstructed image plays a vital role in the field of image processing. Compressive Sampling is an innovative and rapidly growing method for reconstructing signals. It is extensively used in image reconstruction. The literature uses a variety of matching pursuits for image reconstruction. In this paper, we propose a modified method named compressive sampling matching pursuit (CoSaMP) for image reconstruction that promises to sample sparse signals from far fewer observations than the signal’s dimension. The main advantage of CoSaMP is that it has an excellent theoretical guarantee for convergence. The proposed technique combines CoSaMP with curvelet transform for better reconstruction of image. Experiments are carried out to evaluate the proposed technique on different test images. The results indicate that qualitative and quantitative performance is better compared to existing methods.

Recovery of Sparse Signals via Modified Hard Thresholding Pursuit Algorithms

In this paper, we propose a modified version of the hard thresholding pursuit algorithm, called modified hard thresholding pursuit (MHTP), using a convex combination of the current and previous points. The convergence analysis, finite termination properties, and stability of the MHTP are established under the restricted isometry property of the measurement matrix. Simulations are performed in noiseless and noisy environments using synthetic data, in which the successful frequencies, average runtime, and phase transition of the MHTP are considered. Standard test images are also used to test the reconstruction capability of the MHTP in terms of the peak signal-to-noise ratio. Numerical results indicate that the MHTP is competitive with several mainstream thresholding and greedy algorithms, such as hard thresholding pursuit, compressive sampling matching pursuit, subspace pursuit, generalized orthogonal matching pursuit, and Newton-step-based hard thresholding pursuit, in terms of recovery capability and runtime.

Percussion-based loosening detection method for multi-bolt structure using convolutional neural network DenseNet-CBAM

Threaded fasteners are widely applied in mechanical systems, providing the functions of connection, fastening, and sealing. However, loosening is vulnerable to occurring in harsh environment. The importance of loosening detection cannot be emphasized. Percussion-based loosening detection method has attracted much attention due to the convenience and low cost. However, the simultaneous loosening detection of multiple-threaded fasteners based on percussion method is still a challenging issue that needs to be addressed. This study proposes a novel multi-bolt loosening detection method combining percussion method, and deep learning. The method consists of three integrated modules, that is, signal preprocessing, loosening information enhancement, and loosening detection modules. In the first module, variational mode decomposition is used to decompose the original signal into a series of intrinsic mode function to eliminate the interference of noise. In the second module, compressive sampling matching pursuit is applied to represent the denoised signal sparsely, and the sparse signal is fused with the denoised signal to enhance loosening information in the signal. Last, DenseNet-CBAM network structure combining attention mechanism is proposed for multiple classification task. Experimental results showed that the proposed method achieved the detection accuracy of more than 97% in three different types of mechanical structures with multiple-threaded fasteners, indicating its great potentials in engineering applications.

Application of regularization method with sparsity prior in riser vortex-induced vibration reconstruction

In the experimental investigation or in-situ monitoring of the vortex-induced vibration (VIV) of offshore risers, it is often necessary to reconstruct the full-field structural response based on discrete observations. Conventionally, this can be done using the modal decomposition method. However, the method can be invalid with fewer measurements than unknown modes and is unstable when the data contains measurement noises. This study presents a novel sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit (CoSaMP) algorithm. It formulates the reconstruction problem in a regularization framework with a prior related to the sparsity of the modal coordinates, which differs from the classic method that seeks a least-square solution. Verification tests demonstrate that our method outperforms the classic method regarding accuracy and stability, especially when the measurements are noisy and insufficient, highlighting its potential applications in engineering.

Analysis of Sparse Signal Sequences under Compressive Sampling Techniques for Different Measurement Matrices

Introduction:: A more modern, extremely applicable method for signal acquisition is compression sensing. It permits effective data sampling at a rate that is significantly lower than what the Nyquist theorem suggests. Compressive sensing has a number of benefits, including a muchreduced demand for sensory devices, a smaller memory storage need, a greater data transfer rate, and significantly lower power usage. Compressive sensing has been employed in a variety of applications because of all these benefits. Neuro-signal acquisition is a domain in which compressive sensing has applications in the medical industry. Methods:: The novel methods discussed in this article are FFT-based CoSaMP (FFTCoSaMP), DCT-based CoSaMP(DCTCoSaMP) and DWT-based CoSaMP (DWTCoSaMP) based on sparse signal sequences / dictionaries by means of Transform Techniques, where CoSaMP stands for Compressive Sampling Matching Pursuit with respect to Objective Quality Assessment Algorithms like PSNR, SSIM and RMSE, where CoSaMP stands for Compressive Sampling Matching Pursuit. Results: DWTCoSaMP is giving the PSNR values of 40.26 db, for DCTCoSaMP and FFTCoSaMP, PSNR is 36.76 db and 34.76 db. For DWTCoSaMP, SSIM value is 0.8164, and for DCTCoSaMP and FTCoSaMP, SSIM 0.719 and 0.5625 respectively. Finally, for DWTCoSaMP, RMSE value is 0.442, and for DCTCoSaMP and FFTCoSaMP, SSIM 0.44 and 0.4425, respectively. Conclusion:: Among Compressed sampling techniques DWTCoSaMP, DCTCoSaMP and FFTCoSaMP discussed in this paper, DWTCoSaMP reveals the best results.

Operating modal analysis from sub-sampled vibration response based on compressed sensing and FastICA

In order to identify more high order modal from a small amount of vibration response signal sampling, this paper proposes a method for identifying the OMA of sub-sampled vibration response signals based on compression sensing (CS) and fast independent component analysis (FastICA). Firstly, the method subsamples a large number of vibrational signals to retain the original key information of the signal; Secondly, the subsampled signal is restored by using the compressive sampling matching pursuit (CoSaMP) algorithm of the compression-aware reconstruction algorithm. Finally, the source signal is separated by FastICA to obtain the multi-order natural frequencies and modal mode shapes of the structure. According to Shannon’s theorem, if the analog signal is reproduced without distortion, the sampling frequency should be no less than 2 times the highest frequency in the analog signal spectrum. This method can reduce the amount of original signal acquisition and the requirements for the frequency of the sampled signal, and the recovery signal has a high similarity with the original signal and the natural frequency is not changed. It can effectively identify the higher-order modes of the structure on the basis of breaking through the Nyquist sampling frequency. Experimental results of the subsampled vibration response signal on the uniform steel cantilever beam show that the method can reconstruct the original signal from a small number of subsampled vibration response signals, and identify the high-order nature frequency and modal mode shape that break through the Nyquist sampling frequency.

A neighborhood-based multiple orthogonal least square method for sparse signal recovery

Orthogonal least squares (OLS) is a popular greedy algorithm because of its simplicity and low complexity. To improve the reconstruction accuracy performance of OLS, the multiple orthogonal least squares (MOLS) algorithm selects multiple L indices per iteration. Compared with OLS, MOLS improves the reconstruction accuracy and reduces the running time. However, the MOLS algorithm ignores the situation that the correct atom is in the neighborhood of the selected multiple L indices. We propose a neighborhood-based MOLS (NMOLS) algorithm in this study. The NMOLS algorithm incorporates a neighborhood-based strategy to find the more matching atoms in each iteration. NMOLS selects the support from the candidate atoms by comparing their residual error. Simulation and image experimental results show that the proposed algorithm outperforms orthogonal matching pursuit (OMP), regularized OMP (ROMP), compressive sampling matching pursuit (CoSaMP), orthogonal least squares (OLS), and MOLS in terms of reconstruction accuracy.

Restoration of electromechanical admittance signature via solving constrained optimization problems for concrete structural damage identification

Effective restoration of lossy data is prerequisite to guarantee the reliability of early warning information for damage diagnosis, considering large amounts of sensor data to be collected, transmitted and stored in long-term structural health monitoring (SHM) process. In this study, a compressive sampling matching pursuit (CoSaMP) algorithm was developed for solving the restoration problem of electromechanical admittance (EMA, inverse of impedance) signatures-based damage identification. Observed vectors through a random matrix projection were collected as a substitute of the EMA signatures used in conventional method, and EMA signature restorations from incomplete observed vectors were transformed into solving constrained optimization problems. Then the CoSaMP algorithm was utilized to recover EMA signatures with loss in observed vectors. Validation of the approach was conducted by a series of tests on artificial crack identification for a standardized concrete cube under laboratory conditions, which was compared with that using iterative shrinkage-thresholding algorithm (ISTA)-based algorithm. Additionally, impacts of different loss ratios on restoration accuracy were discussed. The proposed approach showed promising availability for damage identification using EMA technique encountered with lossy data.

Three-dimensional ionospheric tomography based on compressed sensing

The insufficient number of low-elevation observations is a limitation of the three-dimensional ionospheric computer tomography (CT) based on the global navigation satellite system (GNSS). To solve this problem, accurate prior information on the regional ionosphere must be obtained. However, it is difficult to explicitly and accurately express prior ionospheric information. This study uses compressed sensing (CS) for ionospheric tomography for the first time. Specifically, the electron density obtained from the international reference ionosphere is used to build a dictionary to fully integrate the prior information into the dictionary. Then, the electron density is reconstructed by using the compressive sampling matching pursuit method. Subsequently, the GNSS data of China (Region I) and Europe (Region II) were utilized to validate this proposed method, and the results are compared with ionosonde observations. The mean and standard deviation (SD) of the difference with respect to the ionosonde result are 41 and 22 km, respectively. The mean and SD of relative deviation were 16% and 9%, respectively. In Region II, the mean and SD of the deviation between the reversed peak electron density and the result of the ionosonde were 1.9 × 1010 m−3 and 8.1 × 1010 m−3, respectively. The mean and SD of the relative deviation were 3% and 13%, respectively. The mean and SD of the peak height deviation were 33 and 19 km, and the mean and SD of the relative deviation were 11% and 7%. The electron density distribution and variation in these two regions showed a local time dependence, and the horizontal gradient of the electron density in the latitude was greater than that in the longitude. Moreover, CT by CS is efficient, taking about 6 s per inversion based on an desktop computer with 16 GB RAM and Intel (R) Core (TM) i7-8700 CPU.

Improved RIP-based bounds for guaranteed performance of two compressed sensing algorithms

Iterative hard thresholding (IHT) and compressive sampling matching pursuit (CoSaMP) are two mainstream compressed sensing algorithms using the hard thresholding operator. The guaranteed performance of the two algorithms for signal recovery was mainly analyzed in terms of the restricted isometry property (RIP) of sensing matrices. At present, the best known bound using the RIP of order 3k for guaranteed performance of IHT (with the unit stepsize) is \({\delta _{3k}} < 1/\sqrt 3 \approx 0.5774\), and the bound for CoSaMP using the RIP of order 4k is δ4k < 0.4782. A fundamental question in this area is whether such theoretical results can be further improved. The purpose of this paper is to affirmatively answer this question and to rigorously show that the above-mentioned RIP bound for guaranteed performance of IHT can be significantly improved to \({\delta _{3k}} < \left( {\sqrt 5 - 1} \right)/2 \approx 0.618\), and the bound for CoSaMP can be improved to δ4k < 0.5102.

Performance analysis of compressive sensing recovery algorithms for image processing using block processing

&lt;p&gt;The modern digital world comprises of transmitting media files like image, audio, and video which leads to usage of large memory storage, high data transmission rate, and a lot of sensory devices. Compressive sensing (CS) is a sampling theory that compresses the signal at the time of acquiring it. Compressive sensing samples the signal efficiently below the Nyquist rate to minimize storage and recoveries back the signal significantly minimizing the data rate and few sensors. The proposed paper proceeds with three phases. The first phase describes various measurement matrices like Gaussian matrix, circulant matrix, and special random matrices which are the basic foundation of compressive sensing technique that finds its application in various fields like wireless sensors networks (WSN), internet of things (IoT), video processing, biomedical applications, and many. Finally, the paper analyses the performance of the various reconstruction algorithms of compressive sensing like basis pursuit (BP), compressive sampling matching pursuit (CoSaMP), iteratively reweighted least square (IRLS), iterative hard thresholding (IHT), block processing-based basis pursuit (BP-BP) based onmean square error (MSE), and peak signal to noise ratio (PSNR) and then concludes with future works.&lt;/p&gt;

Comparison of different sparse dictionaries for compressive sampling

Compressive sampling/compressed sensing (CS) is building on the observation that most of the signals in nature are sparse or compressible concerning some transform domain. And by converse, the same can be reconstructed with high accuracy by making use of far fewer samples than what is required by violating Shannon-Nyquist theorem. Some of the transform techniques like discrete cosine transform, fast fourier transforms discrete wavelet transform, discrete fourier transforms. In this paper, novel CS techniques like FFTCoSAMP, DCTCoSaMP, and DWTCoSaMP are introduced and compared on different sparse transforms for CS in magnetic resonance (MR) images based on sparse signal sequences/dictionaries by means of transform techniques with respect to objective quality assessment algorithms like PSNR, SSIM and RMSE, where CoSaMP stands for compressive sampling matching pursuit. DWTCoSaMP is giving the PSNR values of 37.16 (DB4), 38.12 (Coif3), 38.5 (Sym8), for DCTCoSaMP and FFTCoSaMP, it’s 36.33 and 36.01 respectively. For DWTCoSaMP, SSIM value is 0.81, and for DCTCoSaMP and FFTCoSaMP, it’s 0.73 and 0.7 respectively. And finally, for DWTCoSaMP, RMSE value is 0.66, and for DCTCoSaMP and FFTCoSaMP, it’s 0.53 and 0.41 respectively. DWTCoSaMP reveals the best than rest of the methods and traditional CS techniques by the detailed comparison and analysis.

Channel estimation and data detection schemes for Orthogonal Time Frequency Space massive MIMO systems

Orthogonal Time Frequency Space (OTFS) massive Multiple Input Multiple Output (MIMO) system combines the benefits of massive MIMO and OTFS modulation to improve performance in high-Doppler scenarios. In this paper, Compressive Sampling Matching Pursuit (CoSaMP) channel estimation is proposed for the downlink OTFS massive MIMO system to improve signal reconstruction in high-Doppler scenarios. Furthermore, this paper implements Gauss-Seidel (GS)-based minimum mean square error (MMSE) data detection in uplink OTFS massive MIMO to lower the complexity of matrix inversion in MMSE data detection and match the MMSE data detection performance in the delay-Doppler domain. The computer simulations performed suggest that the performance of the proposed CoSaMP-based channel estimation with interleaving outperforms the previously proposed channel estimator for the system with negligible computational complexity. The simulation results also suggest that the proposed GS-based MMSE data detection technique almost matches the traditional MMSE-based data detection technique's performance at significantly reduced computational complexity cost.

Secure collaborative cognitive radio based on chaotic modulation and compressive sensing

Cognitive radio (CR) is a wireless technology that is used to overcome the spectrum scarcity problem. CR includes several stages, spectrum sensing is the first stage in the CR cycle. Traditional spectrum sensing (SS) techniques have many challenges in the wideband spectrum. CR security is an important problem, since when an attacker from outside the network access the sensing information this produces an increase in sensing time and reduces the opportunities for exploiting vacant band. Compressive sensing (CS) is proposed to capture all the wideband spectrum at the same time to solve the challenges and improve the performance in the traditional techniques and then one of the traditional SS techniques are applied to the reconstructed signal for detection purpose. The sensing matrix is the core of CS must be designed in a way that produces a low reconstruction error with high compression. There are many types of sensing matrices, the chaotic matrix is the best type in terms of security, memory storage, and system performance. Few works in the literature use the chaotic matrix in CS based CR and these works have many challenges: they used sample distance in the chaotic map to generate a chaotic sequence which consumes high resources, they did not take into consideration the security in reporting channel, and they did not measure their works using real primary user (PU) signal of a practical application under fading channel and low SNR values. In this paper, we propose a chaotic CS based collaborative scenario to solve all challenges that have been presented. We proposed a chaotic matrix based on the Henon map and use the differential chaotic shift keying (DCSK) modulation to transmit the measurement vector through the reporting channel to increase the security and improve the performance under fading channel. The simulation results are tested based on a recorded real-TV signal as PU and Compressive Sampling Matching Pursuit (CoSaMP) recovery algorithm under AWGN and TDL-C fading channels in collaborative and non-collaborative scenarios. The performance of the proposed system has been measured using recovery error, mean square error (MSE), derived probability of detection (Pdrec), and sensitivity to initial values. To measure the improvement introduced by the proposed system, it is evaluated in comparison with selected chaotic and random matrices. The results show that the proposed system provides low recovery error, MSE, with high Pdrec, security, and compression under SNR equal to −30 dB in AWGN and TDL-C fading channels as compared to other matrices in the literature.

A better signal recovery method for an urban environment

Communication systems have had such a profound impact on every aspect of humanity. Wireless broadband infrastructures with high throughput and improved spectral efficiency should ensure greater networking and services throughout all areas. Multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) has excessive bandwidth capacity compared with other techniques; also it can be used in high-frequency applications and fast wireless environments. However, accurate channel estimation is a major problem. Compressive sensing is one of the latest techniques that is paying an overwhelming response to wireless communication networks. This can overcome the channel estimation drawbacks of MIMO-OFDM. Compressed sensing's extraordinary qualities have prompted scholars to use it in a variety of certain other domains, and its innumerable applications have a key role in wireless systems. In Compressive sensing, a priori aided compressive sampling matching pursuit (PA-CoSaMP) algorithm is used here to ensure good performance and to optimize the exact mean squared error rate information. This paper gives an overview of MIMO-OFDM, compressive sensing, and the performance evaluation of the proposed algorithm with OFDM. Simulation results gives the recovered signal details and comparison of error rate performance of PA-CoSaMP and conventional OFDM techniques.

Sparsity Signal Detection for Indoor GSSK-VLC System

In this article, the signal detection problem in indoor visible light communication (VLC) system aided by generalized space shift keying (GSSK) is modeled as a sparse signal reconstruction problem, which has lower computational complexity by exploiting the sparse reconstruction algorithms in compressed sensing (CS). In order to satisfy the measurement matrix property to perform sparse signal reconstruction, a preprocessing approach of measurement matrix is proposed based on singular value decomposition (SVD), which theoretically guarantees the feasibility of utilizing CS based sparse signal detection method in indoor GSSK-VLC system. Then, by adopting classical orthogonal matching pursuit (OMP) algorithm and compressed sampling matching pursuit (CoSaMP) algorithm, the GSSK signals are efficiently detected in the considered indoor GSSK-VLC system. Furthermore, a more efficient detection algorithm combined with OMP and maximum likelihood (ML) is also presented especially for SSK scenario. Finally, the effectiveness of the proposed sparsity aided detection algorithms in indoor GSSK-VLC system are verified by computer simulations. The results show that the proposed algorithms can achieve better bit error rate (BER) and lower computation complexity than ML based detection method. Specifically, a signal-to-noise ratio (SNR) gain as high as 12 dB is observed in the SSK scenario and about 5 dB in case of a GSSK scenario upon employing our proposed detection methods.

Millimeter Wave MIMO out Door Channel Estimation and Precoding

Millimeter wave (mm Wave) communications is one of the technologies for 5G cellular systems. In the mm Wave communication, there is a lot of path loss can be reduced by Precoding. The channel state information (CSI) should be known at the transmitting station, in the design of precoding matrices and to get good accuracy in estimating sparse channels a Compressive sensing (CS) based recovery algorithms was used. Not only for good accuracy the algorithm is also used for mm Wave channel estimation for exploiting the mm Wave channel’s sparse in multi-path construction. Hence, in this paper, for mm Wave outdoor channel estimation, the CS recovery methods orthogonal matching pursuit (OMP) and compressive sampling matching pursuit (CoSaMP) are used. The singular value decomposition (SVD) precoding is developed using the estimated channel. By (MSE) mean square error and spectral efficiency which were the performance metrics in channel estimation and precoding were done by using MATLAB simulations to get the efficacy of the OMP and CoSaMP algorithm.