Block Orthogonal Matching Pursuit Algorithm Research Articles

An improved block orthogonal matching pursuit for moving force identification using block-sparse compressed sensing

Moving force identification (MFI) based on compressed sensing (CS) has been proven to be promising in bridge structural health monitoring. Nevertheless, there exist the difficulties in storage and transmission cost of massive monitoring data and the lack of considering the block-sparse features of moving forces in particular transform domains. Inspired by the structural characteristics of sparse representation data, a block-sparse compressed sensing (BSCS) framework is first developed to reconstruct moving forces with block-sparse distribution in the frequency domain. To solve the BSCS equation, an improved block orthogonal matching pursuit algorithm, considering atom screening strategy (ASS-BOMP), is then proposed to ensure that moving forces can still be successfully identified even if the preset block length is inconsistent with the block-sparse features of moving forces. The optimal coherence threshold parameters in the atom screening strategy are determined by the Bayesian information criterion (BIC). Finally, the accuracy and feasibility of the proposed method are validated through numerical simulations and laboratory experiments. The results show that the proposed method can effectively compress response data and accurately identify moving forces distributed in the form of frequency band. Furthermore, the ASS-BOMP algorithm outperforms the traditional BOMP with higher MFI accuracy and robustness.

Research on Distributed Compressed Sensing With Dynamic Block Sparsity for Underwater Acoustic Channel Estimation

Channel estimation plays a crucial role in Internet of Underwater Things networks. Traditional channel estimation algorithms have limited performance improvement under the block-sparsity underwater acoustic channel, and the distributed compressed sensing (DCS) method has not been researched under block-sparsity recovery. In this article, we propose DCS with block sparsity for underwater acoustic channel estimation under short observation length and low SNR scenarios. Specifically, the underwater acoustic channels are partitioned some sub-blocks that have the identical size, and the simultaneous block orthogonal matching pursuit algorithm (SBOMP) is proposed to enhance the channel estimates that have common delays. However, the number of nonzero taps located in a partitioned sub-block does not equal to the size of partitioned sub-blocks, and the channel between adjacent two data blocks may have slightly difference, when the SBOMP algorithm is applied, there would be much estimated noise. In order to address this problem, in this article, we also propose dynamic block sparsity-based SBOMP which is referred to as DSBOMP. The proposed DSBOMP consists of the SBOMP algorithm, first-order derivative of the residual method, and parallel comparison strategy. The first-order derivative is used to remove some negligible taps and dynamically measure the number of significant taps; the parallel comparison strategy is used to check whether the current taps are available. Both simulation and sea trial data indicate that, our proposed SBOMP and DSBOMP algorithms have better channel estimation performance than tradition algorithms under short observation length and low SNR. Moreover, our proposed DSBOMP achieves the best communication performance.

A perturbation analysis based on group sparse representation with orthogonal matching pursuit

Abstract In this paper, by exploiting orthogonal projection matrix and block Schur complement, we extend the study to a complete perturbation model. Based on the block-restricted isometry property (BRIP), we establish some sufficient conditions for recovering the support of the block 𝐾-sparse signals via block orthogonal matching pursuit (BOMP) algorithm. Under some constraints on the minimum magnitude of the nonzero elements of the block 𝐾-sparse signals, we prove that the support of the block 𝐾-sparse signals can be exactly recovered by the BOMP algorithm in the case of ℓ 2 \ell_{2} and ℓ 2 / ℓ ∞ \ell_{2}/\ell_{\infty} bounded total noise if 𝑨 satisfies the BRIP of order K + 1 K+1 with δ K + 1 < 1 K + 1 ⁢ ( 1 + ϵ A ( K + 1 ) ) 2 + 1 ( 1 + ϵ A ( K + 1 ) ) 2 - 1 . \delta_{K+1}<\frac{1}{\sqrt{K+1}(1+\epsilon_{\boldsymbol{A}}^{(K+1)})^{2}}+\frac{1}{(1+\epsilon_{\boldsymbol{A}}^{(K+1)})^{2}}-1. In addition, we also show that this is a sharp condition for exactly recovering any block 𝐾-sparse signal with the BOMP algorithm. Moreover, we also give the reconstruction upper bound of the error between the recovered block-sparse signal and the original block-sparse signal. In the noiseless and perturbed case, we also prove that the BOMP algorithm can exactly recover the block 𝐾-sparse signal under some constraints on the block 𝐾-sparse signal and δ K + 1 < 2 + 2 2 ⁢ ( 1 + ϵ A ( K + 1 ) ) 2 - 1 . \delta_{K+1}<\frac{2+\sqrt{2}}{2(1+\epsilon_{\boldsymbol{A}}^{(K+1)})^{2}}-1. Finally, we compare the actual performance of perturbed OMP and perturbed BOMP algorithm in the numerical study. We also present some numerical experiments to verify the main theorem by using the completely perturbed BOMP algorithm.

Imaging Algorithm for Sea-Surface Ship Targets Based on Block Sparsity

In this study, a phased array radar was used to accurately image stationary and moving ship targets on the vast sea surface. To solve the challenge in real-time processing of the massive amount of data generated by phased array synthetic-aperture radar imaging, this study leveraged the block sparse characteristics of ships on the sea surface and adopted the joint block orthogonal matching pursuit algorithm to obtain high-resolution one-dimensional range images. By only estimating the azimuth Doppler parameters of the targets within the range gates, the amount of process data was significantly reduced, and the data processing speed was enhanced. The synchrosqueezing transform-STFT algorithm was introduced to perform transient imaging as a solution to the blurred imaging of ships due to the three-dimensional swing under the action of waves. The images of the targets were obtained from different squint angles of the antenna array, which improved the imaging accuracy of ships on a vast sea surface. Compared with traditional imaging algorithms, this algorithm can effectively overcome the interference of sea clutter on ship imaging and the influence of sea waves on ship wobble; it can also obtain high-resolution imaging for both stationary and moving targets in a limited amount of time.

Study on computer vision target tracking algorithm based on sparse representation

Video target tracking covers a variety of interdisciplinary subjects such as pattern recognition, image processing, computer graphics and artificial intelligence. In recent years, visual tracking research methods have made significant progress, and scholars have proposed many excellent algorithms. Based on this, this paper uses the basic tracking algorithm and block orthogonal matching pursuit (BOMP) algorithm of image reconstruction, respectively, from the run time, the quality of reconstruction, reconstruction error of the two algorithms to do simulation experiments, and compare their performance, the results show that the BOMP algorithm running time is short, has extensive application, therefore, to determine the BOMP algorithm as a sparse representation model is the core of the method. Then establish the target observation model, introduce the sparse display into the particle filter framework, and update the sparse representation coefficients so that the norm reaches the optimal solution and ensure the accuracy of the tracking target. Finally, through the simulation experiment, the success rate of the target coverage is calculated. The results show that the BOMP algorithm can maintain high tracking accuracy and strong stability in the case of appearance changes caused by illumination changes, partial occlusion and attitude changes.

Stokes parameters and DOA estimation for nested polarization sensitive array in unknown nonuniform noise environment

To obtain a large aperture for improving parameter estimation performance, this paper introduces a novel polarization sensitive array composed of augmented and optimally nested subarrays with differently oriented antennas, and then proposes an algorithm for direction of arrival (DOA) and Stokes parameter estimation of completely and partially polarized signals, in unknown nonuniform noise environment and without source number knowledge. The aperture of the proposed array significantly increases since the difference co-array of the optimally nested subarray can obtain the maximum degrees of freedom. There is a systematic procedure to determine the numbers of antennas in the two subarrays in order to obtain similar apertures for the two subarrays. Unfortunately, both the difference co-arrays of the optimally nested subarray and between the two subarrays have holes, which degrades performance of parameter estimation. By using oblique projection operators, the proposed algorithm first fills the holes and suppresses the nonuniform noise to obtain hole-free and noiseless difference co-arrays, and then the difference co-arrays are employed to form a block-sparsity model. Finally, based on the model, block orthogonal matching pursuit algorithm is used for parameter estimation. The Cramér-Rao bound and its existence condition are derived. Simulation results are given to demonstrate the superior performance of the proposed array and method.

BSBL-Based DOA and Polarization Estimation with Linear Spatially Separated Polarization Sensitive Array

The problem of multiple incident signals’ direction of arrival (DOA) and polarization estimation with linear spatially separated polarization sensitive array (SS-PSA) is investigated in sparse Bayesian learning (SBL) framework. SS-PSA is widely studied due to its low mutual coupling compared with the spatially collocated polarization sensitive array. On the one hand, the sparse representation of data model of proposed array can be expressed skillfully as a block-sparse representation. On the other hand, block sparse Bayesian learning (BSBL) algorithm has excellent performance in recovering the block-sparse signals. Therefore, in this paper, BSBL algorithm is extended to SS-PSA for DOA and polarization estimation. Firstly, a sparse representation model without parameters coupling is established, where the sparse coefficient vector is a block-sparse signal. Secondly, the expectation–maximization method in BSBL framework, i.e., BSBL-EM algorithm, is proposed to recover the block-sparse signal. Lastly, angles estimation can be obtained from the recovered sparse signal according to the intra-block correlation. Simulation results demonstrate that the BSBL-EM algorithm used in DOA and polarization estimation with SS-PSA exhibits better performance compared with Block Orthogonal Matching Pursuit algorithm and Group Basis Pursuit.

Through‐the‐wall radar imaging algorithm for moving target under wall parameter uncertainties

In order to solve the problems of slow imaging speed and poor reconstruction accuracy of wall parameters under the condition of wall parameter fuzziness, an improved limited Broyden–Fletcher–Goldfarb–Shanno-particle swarm optimisation (LBFGS-PSO) algorithm was proposed. The LBFGS-PSO algorithm model solves the problems of slow calculation speed and large errors of the traditional quasi-Newton algorithm and particle swarm algorithm. The algorithm combined with block orthogonal matching pursuit algorithm can not only accurately reconstruct the position of the sidewall, but also can use the multi-path information to accurately reconstruct the moving target and the stationary target. Compared with the traditional BFGS algorithm and PSO algorithm, the proposed algorithm can reduce the calculation time and provide more accurate estimation results. Simulation results and data analysis verify the performance of the proposed algorithm.

Tomography synthetic aperture radar imaging based on extended block orthogonal matching pursuit algorithm

The compressed sensing (CS)-based methods for tomography synthetic aperture radar (SAR) imaging have a good performance in the case of a large number of baselines. Unfortunately, for the current tomography SAR, the baselines are obtained in repeat-pass mode from a large number of parallel passes in the same scene. That is expensive and can be severely affected by temporal decorrelation. And the performance of CS-based methods degrades rapidly with the decrease of the number of baselines. Inspired by the block-sparsity theory, an extended block orthogonal matching pursuit algorithm by using the weighted operation and a new column-block selection strategy is proposed for tomography SAR imaging. By using neighboring pixels information in reconstruction, the proposed method can improve the performance of CS-based methods in the case of strong noise and a small number of baselines. Experimental results confirm the effectiveness of the proposed method.

Perturbed block orthogonal matching pursuit

The block orthogonal matching pursuit (BOMP) algorithm is an efficient method in compressed sensing (CS) for the reconstruction of block-sparse signals, whose non-zero entries occur in clusters. However, due to the non-ideal factors in practice, there exits perturbation in the CS system, which may cause significant performance degradation during reconstruction. In this Letter, a perturbed BOMP algorithm is presented to deal with this problem, which extends BOMP algorithm to the perturbation case. The proposed algorithm performs controlled perturbation on each selected block of support vectors to decrease the orthogonal residual at each iteration. Moreover, the condition of successful reconstruction is derived. Simulation results demonstrate the effectiveness and robustness of the proposed algorithm.

Block Sparse Bayesian Learning Based Joint User Activity Detection and Channel Estimation for Grant-Free NOMA Systems

This paper concerns uplink grant-free nonorthogonal multiple access, where the handshaking procedure is not required to reduce control signaling overhead and transmission latency. In especially the dynamic scenarios, e.g., Internet of vehicles, the active users have to be identified and their channel state information needs to be estimated before performing multiuser detection. We investigate the joint user activity detection (UAD) and channel estimation (CE), which provides necessary information for data detection. In this paper, the joint UAD and CE is formulated as a block sparse signal recovery problem. First, the block orthogonal matching pursuit (BOMP) algorithm is studied for this problem, but its complexity grows with the fourth power of active user number, which hinders its application. Then, block sparse Bayesian learning (BSBL) is investigated to solve this problem, and in particular a low complexity message passing based implementation of BSBL with belief propagation and mean field is developed. The proposed message passing based BSBL (MP-BSBL) algorithm has a complexity independent of active user number, which can be significantly lower than that of the BOMP algorithm. In addition, MP-BSBL provides an estimate of the noise power, which can be readily used for data detection. Simulation results show that the MP-BSBL algorithm delivers almost the same performance as BOMP with the exact knowledge of active user number and can reach the performance bound for channel estimation.

Time-Angle Domain Sparsity-Based MIMO Channel Estimation Approach in High Mobility Scenarios

This letter investigates the sparse channel estimation approach for multiple input multiple output systems in high mobility scenarios. The large quantity of channel estimation coefficients is significantly reduced by taking advantage of both the channel sparsity in time-angle domain and the basis expansion model for time-varying channel. After the establishment of the structured compressive sensing model, a Newton auxiliary block orthogonal matching pursuit algorithm is put forward to recover the channel. It is illustrated in the numerical simulation results that the proposed approach has excellent performance and outperforms the traditional counterparts.

An Optimal Condition for the Block Orthogonal Matching Pursuit Algorithm

Recovery of the support of a block $K$ -sparse signal ${{x}}$ from a linear model ${{y}}= {A} {{x}} + {v}$ , where ${A}$ is a sensing matrix and ${v}$ is a noise vector, arises from many applications. The block orthogonal matching pursuit (BOMP) algorithm is a popular block sparse recovery algorithm and has received much attention in the recent decade. It was proved by Eldar et al. that the BOMP can recover the positions $\Omega $ of the nonzero blocks of any block $K$ -sparse vector ${{x}}$ with a block length $d$ in the noisy case (under certain condition on ${{x}}$ and ${v}$ ) and can exactly recover ${{x}}$ in the noiseless case in $K$ iterations if the block mutual coherence $\mu ({A})$ and sub-coherence $\nu ({A})$ of ${A}$ satisfy $(2K-1)d\mu ({A}) +(d-1) \nu ({A}) In this paper, we first improve and develop sufficient conditions of recovering $\Omega $ with the BOMP algorithm under the $\ell _{2}$ -bounded and $\ell _{\infty }$ -bounded noises, respectively. Then, we show that for any given positive integers $K$ and $d$ , there always exist a block $K$ -sparse vector ${{x}}$ with the block length $d$ , and a sensing matrix ${A}$ with $(2K-1)d\mu ({A}) + (d-1) \nu ({A})=1 $ such that the BOMP is not able to recover ${{x}}$ from ${{y}}= {A} {{x}} $ in $K$ iterations. This indicates that the condition proposed by Eldar et al. is sharp in terms of the condition on ${A}$ .

Recovery of block sparse signals under the conditions on block RIC and ROC by BOMP and BOMMP

In this paper, we consider the block orthogonal matching pursuit (BOMP) algorithm and the block orthogonal multi-matching pursuit (BOMMP) algorithm respectively to recover block sparse signals from an underdetermined system of linear equations. We first introduce the notion of block restricted orthogonality constant (ROC), which is a generalization of the standard restricted orthogonality constant, and establish respectively the sufficient conditions in terms of the block RIC and ROC to ensure the exact and stable recovery of any block sparse signals in both noiseless and noisy cases through the BOMP and BOMMP algorithm. We finally show that the sufficient condition on the block RIC and ROC is sharp for the BOMP algorithm.

Structured Compressive Sensing-Based Channel Estimation for Time Frequency Training OFDM Systems Over Doubly Selective Channel

This letter proposes a novel doubly selective channel estimation scheme based on structured compressive sensing (SCS) for time-frequency training orthogonal frequency division multiplexing systems. By exploiting the proposed pilot pattern, an SCS model is built by utilizing the jointly sparse property of the coefficient vectors corresponding to the channel expansion bases. The doubly selective channel can be recovered through the proposed adaptive support-aware block orthogonal matching pursuit algorithm. Simulation results demonstrate that the proposed scheme has superior performance than conventional counterparts over doubly selective channel with lower computational complexity.

Successive Hypothesis Testing Based Sparse Signal Recovery and Its Application to MUD in Random Access

Based on successive hypothesis testing, we propose an approach for sparse signal recovery and apply it to random access to detect multiple block-sparse signals over frequency-selective fading channels. By introducing the sparsity variable, the proposed approach decides the presence or absence of the signal in each stage. To mitigate the error propagation, adaptive ordering is also employed as a greedy algorithm. From simulation results, it is shown that the proposed approach performs better than the block orthogonal matching pursuit algorithm, which is a well-known greedy compressive sensing algorithm for compressive random access.

Beam-Blocked Channel Estimation for FDD Massive MIMO With Compressed Feedback

To fully exploit both multiplexing gain and array gain of massive multiple-input–multiple-output (MIMO), the channel state information must be obtained accurately at transmitter side (CSIT). However, conventional channel estimation solutions are not suitable for frequency-division duplexing (FDD) multiuser massive MIMO because of overwhelming pilot and feedback overhead. To reduce the pilot and feedback overhead of channel estimation in FDD systems, we propose a compressive channel estimation scheme for FDD massive MIMO systems in this paper, where the beam-blocked sparsity of massive MIMO channels in beamspace is leveraged. Particularly, we first propose a beam-blocked compressive channel estimation scheme, which can reduce the overhead for downlink training. Then, an optimal block orthogonal matching pursuit algorithm at the BS is proposed to acquire reliable CSIT from the limited number of pilots. Furthermore, an efficient algorithm for channel matrix recovery from separately quantized amplitude and phase of received signals is developed to efficiently decrease feedback load. Simulation results demonstrate that our proposed scheme outperforms conventional solutions.

Many Access for Small Packets Based on Precoding and Sparsity-Aware Recovery

Modern mobile terminals produce massive small data packets. For these short-length packets, it is inefficient to follow the current multiple access schemes to allocate transmission resources due to heavy signaling overhead. We propose a non-orthogonal many-access scheme that is well suited for the future communication systems equipped with many receive antennas. The system is modeled as having a block-sparsity pattern with unknown sparsity level (i.e., unknown number of transmitted messages). Block precoding is employed at each single-antenna transmitter to enable the simultaneous transmissions of many users. The number of simultaneously served active users is allowed to be even more than the number of receive antennas. Sparsity-aware recovery is designed at the receiver for joint user detection and symbol demodulation. To reduce the effects of channel fading on signal recovery, normalized block orthogonal matching pursuit (BOMP) algorithm is introduced, and based on its approximate performance analysis, we develop interference cancellation based BOMP (ICBOMP) algorithm. The ICBOMP performs error correction and detection in each iteration of the normalized BOMP. Simulation results demonstrate the effectiveness of the proposed scheme in small packet services, as well as the advantages of ICBOMP in improving signal recovery accuracy and reducing computational cost.

Compressive sensing based joint frequency offset and channel estimation for OFDM

We consider joint estimation of carrier frequency offset (CFO) and channel impulse response (CIR) for orthogonal frequency division multiplexing (OFDM) with pilot symbols. A new method based on compressed sensing is proposed. It has been shown that the CIR can be represented as a 1-block sparse signal by using a dictionary constructed by concatenating subspaces of CFO values taken from a search space. Recovery of both CFO and CIR is accomplished by the block orthogonal matching pursuit algorithm. The proposed method uses only one OFDM training block and does not require any initialization. The performance of the proposed method is compared against the well-established pilot based estimators: Moose, Classen, the maximum likelihood estimator, and the p-algorithm. Numerical results show that the performance of the proposed method does not depend on the value of the CFO. We also give worst-case upper bounds for the mean squared error of the CIR estimate for a sparse multipath channel.

Sensing and measurement dictionaries design for block OMP algorithm

The block orthogonal matching pursuit (BOMP) algorithm aims to recover block sparse signals whose non-zero components have a block structure. Sensing and measurement dictionaries are alternatively optimised to have small inter- and sub-block mutual coherences. The computational complexity of the proposed algorithm is low. With the designed dictionaries, the performance of the BOMP algorithm improves.