Compressive Sampling Matching Pursuit Algorithm Research Articles

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.

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.

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.

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.

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.

A New Design of Codebook for Hybrid Precoding in Millimeter-Wave Massive MIMO Systems

The precoding scheme based on codebooks is used to save the same set of codebook in advance at the transmitter and the receiver, then, the receiver selects the most appropriate precoding matrix from codebooks according to different channel state information (CSI). Therefore, the design of codebook plays an important role in the performance of the whole scheme. The symmetry-based hybrid precoder and combiner is a highly energy efficient structure in the millimeter-wave massive multiple-input multiple-output (MIMO) system, but at the same time, it also has the problems of high bit error rate and low spectral efficiency. In order to improve the spectral efficiency, we formulate the codebook design as a joint optimization problem and propose an iteration algorithm to obtain the enhanced codebook by combining the compressive sampling matching pursuit (CoSaMP) algorithm with the dictionary learning algorithm. In order to prove the validity of the proposed algorithm, we simulate and analyze the change of the spectral efficiency of the algorithm with the signal-to-noise ratio (SNR) and the number of radio frequency (RF) chains of different precoding schemes. The simulation results demonstrate that the spectral efficiency of the algorithm is obviously outstanding compared with that of the OMP-based joint codebook algorithm and the hybrid precoding algorithm with quantization algorithm under low SNR and different numbers of RF chains. Particularly, when SNR is lower than 0 dB, the proposed algorithm performs very close to the optimal unconstrained precoding algorithm.

ANN-Assisted CoSaMP Algorithm for Linear Electromagnetic Imaging of Spatially Sparse Domains

Greedy pursuit algorithms (GPAs) are widely used to reconstruct sparse signals. Even though many electromagnetic (EM) inverse scattering problems are solved on sparse investigation domains, GPAs have rarely been used for this purpose. This is because (i) they require a priori knowledge of the sparsity level in the investigation domain, which is often not available in EM imaging applications, and (ii) the EM scattering matrix does not satisfy the restricted isometric property. In this work, these challenges are respectively addressed by (i) using an artificial neural network (ANN) to estimate the sparsity level, and (ii) adding a Tikhonov regularization term to the diagonal elements of the scattering matrix. These enhancements permit the compressive sampling matching pursuit (CoSaMP) algorithm to be efficiently used to solve the two-dimensional EM inverse scattering problem, which is linearized using the Born approximation, on spatially sparse investigation domains. Numerical results, which demonstrate the efficiency and applicability of the proposed ANN-enhanced CoSaMP algorithm, are provided.

An Improved CoSaMP Multiuser Detection for Uplink Grant Free NOMA System

Non-Orthogonal Multiple Access (NOMA) is the most prominent technology that enhances massive connectivity and spectral efficiency in 5G cellular communication. It provides services to the multi-users in time, frequency, and code domain with significant power level. Message Passing Algorithm (MPA) detection in a multi-user uplink grant-free system requires user activity information at the receiver that makes it impractical. To circumvent this problem, (MPA) is combined with Compressed Sensing (CS) based detection which not only detects the user activity but also the signal data. However, the Compressive Sampling Matching pursuit (CoSaMP) algorithm uses Zero Forcing (ZF) detector to estimate the signal but its performance degrades with increment in Signal to Noise Ratio (SNR). Therefore, Minimum Mean Square Error (MMSE) detector in CoSaMP algorithm is deployed in this paper that enhances detection accuracy and BER performance. The simulation results validate that the proposed algorithm attains better performance than MPA and conventional CoSaMP algorithm in high SNR.

Channel estimation via gradient pursuit for mmWave massive MIMO systems with one-bit ADCs

In millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, 1 bit analog-to-digital converters (ADCs) are employed to reduce the impractically high power consumption, which is incurred by the wide bandwidth and large arrays. In practice, the mmWave band consists of a small number of paths, thereby rendering sparse virtual channels. Then, the resulting maximum a posteriori (MAP) channel estimation problem is a sparsity-constrained optimization problem, which is NP-hard to solve. In this paper, iterative approximate MAP channel estimators for mmWave massive MIMO systems with 1 bit ADCs are proposed, which are based on the gradient support pursuit (GraSP) and gradient hard thresholding pursuit (GraHTP) algorithms. The GraSP and GraHTP algorithms iteratively pursue the gradient of the objective function to approximately optimize convex objective functions with sparsity constraints, which are the generalizations of the compressive sampling matching pursuit (CoSaMP) and hard thresholding pursuit (HTP) algorithms, respectively, in compressive sensing (CS). However, the performance of the GraSP and GraHTP algorithms is not guaranteed when the objective function is ill-conditioned, which may be incurred by the highly coherent sensing matrix. In this paper, the band maximum selecting (BMS) hard thresholding technique is proposed to modify the GraSP and GraHTP algorithms, namely, the BMSGraSP and BMSGraHTP algorithms, respectively. The BMSGraSP and BMSGraHTP algorithms pursue the gradient of the objective function based on the band maximum criterion instead of the naive hard thresholding. In addition, a fast Fourier transform-based (FFT-based) fast implementation is developed to reduce the complexity. The BMSGraSP and BMSGraHTP algorithms are shown to be both accurate and efficient, whose performance is verified through extensive simulations.

Underwater Acoustic Sparse Channel Estimation Based on DW-SACoSaMP Reconstruction Algorithm

The compressive sampling matching pursuit (CoSaMP) algorithm is widely used in orthogonal frequency division multiplexing (OFDM) underwater acoustic (UWA) sparse channel estimation with good estimation accuracy. However, the algorithm requires channel sparsity a priori information as well as a large number of columns in the measurement matrix because of the large delay of the UWA channel during channel estimation, which greatly increases the complexity of CoSaMP. Therefore, a sparsity adaptive CoSaMP based on a dynamic threshold and weak selection of atoms (DW-SACoSaMP) is proposed in this letter. The algorithm can quickly estimate the channel impulse response (CIR) without channel sparsity when used for UWA sparse channel estimation. Simulation results show that, compared with other reconstruction algorithms, the estimation accuracy of this algorithm is higher and the complexity is lower; when the signal to noise ratio (SNR) is greater than 8dB, the advantage of estimation accuracy is more obvious.

On Recovery of Block Sparse Signals via Block Compressive Sampling Matching Pursuit

Compressive sampling matching pursuit (CoSaMP) is an efficient reconstruction algorithm for sparse signal. When the signal is block sparse, i.e., the non-zero elements are presented in clusters, some block sparse reconstruction algorithms have been proposed accordingly. In this paper, we present a new block algorithm based on CoSaMP, called block compressive sampling matching pursuit (BlockCoSaMP). Compared with CoSaMP algorithm, the proposed algorithm shows improved performance when sparse signal is presented in block form. Restricted isometry property (RIP) of measurement matrix is an effective tool for analyzing the performance of the CS algorithm, and Block restricted isometry property (Block RIP) is the extension of traditional RIP. Based on the Block RIP, we derive the sufficient condition to guarantee the convergence of Block-CoSaMP algorithm. In addition, the number of required iterations is obtained. Finally, simulation experiments show that with the increase of block length, the performance of Block-CoSaMP algorithm approaches to that of block subspace pursuit (Block-SP) algorithm. When the block length and sparsity are small, the performance of Block-CoSaMP algorithm is better than that of the CoSaMP, l 2 /l 1 norm and block orthogonal matching pursuit (BOMP) algorithms. Especially, when compared with CoSaMP and l 2 /l 1 norm algorithms, the proposed algorithm exhibits more obvious performance gain.

A Fuzzy Selection Compressive Sampling Matching Pursuit Algorithm for its Practical Application

In compressive sampling matching pursuit algorithm, it requires that the sparsity information of original signal to control the size of the preliminary atomic set and the maximum number of the algorithm iteration. This weakens the reconstruction accuracy, increases the computation complexity and limits its practical application capacity. To overcome the problem, an improved method is proposed. The proposed method firstly sets a fixed step-size as the assumed sparsity to expand the preliminary atomic set at the initial stage when the sparsity information is unknown. Secondly, the proposed algorithm adopts the fuzzy threshold strategy to select the more relevant atoms from the preliminary atomic set to expand the candidate atomic set. Finally, the double threshold control method, multiply stages setting and variable step-size method are used to control the iteration stop condition and adjust the estimated sparsity. When the two threshold iteration stop conditions are simultaneously satisfied, the iteration stops, which shows that the reconstructed signal better approximated the original signal, and the reconstruction performance is the best. Otherwise, if only one of the conditions is satisfied, the size of the estimated sparsity is increased by the variable step size method to reduce the error between the reconstructed signal and original signal. In addition, we extended the proposed algorithm to the multiple measurement vectors scenario for joint sparse signal recovery. Simulation results indicate that the proposed algorithm is better than the other method in terms of the reconstruction performance in single measurement vector and multiple measurement vector cases.

Generalizing CoSaMP to signals from a union of low dimensional linear subspaces

The idea that signals reside in a union of low dimensional subspaces subsumes many low dimensional models that have been used extensively in the recent decade in many fields and applications. Until recently, the vast majority of works have studied each one of these models on its own. However, a recent approach suggests providing general theory for low dimensional models using their Gaussian mean width, which serves as a measure for the intrinsic low dimensionality of the data. In this work we use this novel approach to study a generalized version of the popular compressive sampling matching pursuit (CoSaMP) algorithm, and to provide general recovery guarantees for signals from a union of low dimensional linear subspaces, under the assumption that the measurement matrix is Gaussian. We discuss the implications of our results for specific models, and use the generalized algorithm as an inspiration for a new greedy method for signal reconstruction in a combined sparse-synthesis and cosparse-analysis model. We perform experiments that demonstrate the usefulness of the proposed strategy.

Inner–Outer Support Set Pursuit for Distributed Compressed Sensing

We address the distributed compressed sensing problem of reconstructing a sequence of jointly sparse signals under the condition of an inaccurate and insufficient estimate of the common support set. Correlations between the jointly sparse signals are modeled by the joint sparsity model 1 (JSM-1). We propose a novel algorithm, namely inner–outer support set pursuit (IOSSP), which removes the impact of the estimated common support set, to reduce the computing time as well as the reconstruction error. The IOSSP algorithm divides the support set of each individual sparse signal into two disjoint sets: an inner support set and an outer support set. Two separate procedures, the outer support set pursuit and inner support set pursuit, are then utilized to estimate the outer and inner support sets. We provide the convergence performance of the IOSSP algorithm in both the noiseless and noisy conditions. For the noiseless case, we derive the condition on the estimated common support set, which guarantees an exact reconstruction. For the noisy case, a bound of the reconstruction error is provided, and the derivation process is inspired by the compressive sampling matching pursuit algorithm. The experimental and simulation results demonstrate that the proposed IOSSP algorithm is superior on reconstruction error and computing time over the conventional algorithms for JSM-1, e.g., the parallel pursuit with side information and joint recovery strategy algorithms.

A new greedy algorithm for sparse recovery

Abstract Compressed sensing (CS) has been one of the great successes of applied mathematics in the last decade. This paper proposes a new method, combining the advantage of the Compressive Sampling Matching Pursuit (CoSaMP) algorithm and the Quasi–Newton Iteration Projection (QNIP) algorithm, for the recovery of sparse signal from underdetermined linear systems. To get the new algorithm, Quasi–Newton Projection Pursuit (QNPP), the least-squares technique in CoSaMP is used to accelerate convergence speed and QNIP is modified slightly. The convergence rate of QNPP is studied, under a certain condition on the restricted isometry constant of the measurement matrix, which is smaller than that of QNIP. The fast version of QNPP is also proposed which uses the Richardson’s iteration to reduce computation time. The numerical results show that the proposed algorithms have higher recovery rate and faster convergence speed than existing techniques.

A new method of power system fault recording based on compressed sensing

Wavelet transform is usually used to deal with the numerous data in fault recording of power systems, but it still needs to sample the signal with a high frequency first and then compress the data obtained. In order to solve the problem, this paper proposes a new fault recording method based on compressed sensing theory. The method can break the limit of Nyquist sampling theorem and acquire the fault signal with a much lower sampling frequency. It presents the theoretical framework of compressed sensing, analyzes the characteristics of the faulty waveform, and proposes a new sparsity adaptive and compressive sampling matching pursuit algorithm to reconstruct the fault signal. Finally, simulation results in MATLAB show that the proposed method performs well at different compression ratios in terms of the norm mean‐square error, signal‐to‐noise ratio, and waveform similarity. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Radar Signal Recovery using Compressive Sampling Matching Pursuit Algorithm

In this study, we propose compressive sampling matching pursuit (CoSaMP) algorithm for sub-Nyquist based electronic warfare (EW) receiver system. In compressed sensing (CS) theory time-frequency plane localisation and discretisation into a N×N grid in union of subspaces is established. The train of radar signals are sparse in time and frequency can be under sampled with almost no information loss. The CS theory may be applied to EW digital receivers to reduce sampling rate of analog to digital converter; to improve radar parameter resolution and increase input bandwidth. Simulated an efficient approach for radar signal recovery by CoSaMP algorithm by using a set of various sample and different sparsity level with various radar signals. This approach allows a scalable and flexible recovery process. The method has been satisfied with data in a wide frequency range up to 40 GHz. The simulation shows the feasibility of our method.

Auto Regulated Data Provisioning Scheme with Adaptive Buffer Resilience Control on Federated Clouds

We investigate the channel state information (CSI) in multi-input multi-output (MIMO) cooperative networks that employ the amplify-and-forward transmission scheme. Least squares and expectation conditional maximization have been proposed in the system. However, neither of these two approaches takes advantage of channel sparsity, and they cause estimation performance loss. Unlike linear channel estimation methods, several compressed channel estimation methods are proposed in this study to exploit the sparsity of the MIMO cooperative channels based on the theory of compressed sensing. First, the channel estimation problem is formulated as a compressed sensing problem by using sparse decomposition theory. Second, the lower bound is derived for the estimation, and the MIMO relay channel is reconstructed via compressive sampling matching pursuit algorithms. Finally, based on this model, we propose a novel algorithm so called sparsity adaptive expectation maximization (SAEM) by using Kalman filter and expectation maximization algorithm so that it can exploit channel sparsity alternatively and also track the true support set of time-varying channel. Kalman filter is used to provide soft information of transmitted signals to the EM-based algorithm. Various numerical simulation results indicate that the proposed sparse channel estimation technique outperforms the previous estimation schemes.

On the number of iterations for convergence of CoSaMP and Subspace Pursuit algorithms

In compressive sensing, one important parameter that characterizes the various greedy recovery algorithms is the iteration bound which provides the maximum number of iterations by which the algorithm is guaranteed to converge. In this letter, we present a new iteration bound for the compressive sampling matching pursuit (CoSaMP) algorithm by certain mathematical manipulations including formulation of appropriate sufficient conditions that ensure passage of a chosen support through the two selection stages of CoSaMP, “Augment” and “Update”. Subsequently, we extend the treatment to the subspace pursuit (SP) algorithm. The proposed iteration bounds for both CoSaMP and SP algorithms are seen to be improvements over their existing counterparts, revealing that both CoSaMP and SP algorithms converge in fewer iterations than suggested by results available in literature. • Presents new iteration bounds for CoSaMP and subspace pursuit (SP) algorithms. • Proposed bounds are lesser than their counterparts existing in literature. • The reduction is significant for moderately large K , i.e., system sparsity. • New results on convergence behavior of CoSaMP and SP algorithms presented.

Compressive sampling-based CFO-estimation with exploited features

Based on the compressed sensing (CS) technique, the carrier frequency offset (CFO) is estimated in compressive sampling scenarios. We firstly confirm the compressibility of estimation metric vector (EMV) of conventional maximum likelihood (ML)-based CFO estimation, and thus conduct the compressive sampling at receiver. By exploiting the EMV features, introducing a circle cluster, and proposing a novel coherence-pattern, we then form a feature-aided weight coherence (FAWC) optimization to optimize measurement-matrix. Besides the proposed FAWC optimization, by referencing compressive sampling matching pursuit (CoSaMP) algorithm and exploiting EMV features, a metric-feature based CoSaMP (MFB-CoSaMP) algorithm is proposed to improve the EMV-reconstruction accuracy, and to reduce computational complexity of classic CoSaMP. With reconstructed EMV, we finally develop a CFO estimation method to estimate the coarse CFO and fine CFO. Relative to weighted coherence minimization (WCM) and classic CoSaMP, the elaborate performance evaluations show that the FAWC and MFB-CoSaMP can independently or jointly improve accuracy of the CFO-estimation (including coarse CFO-estimation and fine CFO-estimation), and the improvement is robust to system parameters, e.g., sparsity level, number of measurements, etc. Furthermore, the mean squared error (MSE) of proposed CFO estimation method can almost reach to its Cram e $\acute {\texttt {e}}$ r-Rao lower Bound (CRLB) when a relative large number of measurements, a relative high carrier-to-noise ratio (CNR), and a reasonable length of observed signals can be obtained.