Block Sparsity Research Articles

Blade tip timing for monitoring crack propagation of rotor blades using Block-AOLS

Blade tip timing (BTT) as a non-contact measurement technique can identify the blade vibration parameters. However, the signal recorded by BTT usually does not satisfy the Nyquist sampling theorem. To monitor blade crack propagation, it is important to accurately reconstruct the BTT signal to track the natural frequency shift of the rotor blade. In this paper, a sparse reconstruction method named block-accelerated orthogonal least-squares (Block-AOLS) is proposed to reconstruct the undersampled BTT signal in the time-frequency domain. Block-AOLS not only inherits the advantage of the high accuracy of AOLS but also makes use of the characteristic of block sparsity to reduce the interference components in the BTT signal. Furthermore, Block-AOLS is used to reconstruct the undersampled BTT signal to track the natural frequencies of cracked blades. The advantage of Block-AOLS is illustrated through simulation by comparing with the classical orthogonal matching pursuit. In the spin testing, the vibration of a blisk with eight blades is measured by both BTT and strain gauges, where two symmetrical blades without artificial cracks suddenly broke. The process of crack propagation can be inferred according to the shift of natural frequencies between the perfect and cracked blades. Moreover, a vibration frequency prediction method is provided to avoid comparing the natural frequencies among different blades for crack propagation monitoring, which is suitable to monitor the mistuning blades. To verify the reliability of the crack propagation monitoring using BTT, the strain signal with interval sample is analyzed by synchroextracting transform. Compared the natural frequency of the perfect blade with that of the cracked blade, the time when the natural frequency of the cracked blade shift is the same as that of the BTT result.

A Regional Smoothing Block Sparse Bayesian Learning Method With Temporal Correlation for Channel Selection in P300 Speller.

The P300-based brain–computer interfaces (BCIs) enable participants to communicate by decoding the electroencephalography (EEG) signal. Different regions of the brain correspond to various mental activities. Therefore, removing weak task-relevant and noisy channels through channel selection is necessary when decoding a specific type of activity from EEG. It can improve the recognition accuracy and reduce the training time of the subsequent models. This study proposes a novel block sparse Bayesian-based channel selection method for the P300 speller. In this method, we introduce block sparse Bayesian learning (BSBL) into the channel selection of P300 BCI for the first time and propose a regional smoothing BSBL (RSBSBL) by combining the spatial distribution properties of EEG. The RSBSBL can determine the number of channels adaptively. To ensure practicality, we design an automatic selection iteration strategy model to reduce the time cost caused by the inverse operation of the large-size matrix. We verified the proposed method on two public P300 datasets and on our collected datasets. The experimental results show that the proposed method can remove the inferior channels and work with the classifier to obtain high-classification accuracy. Hence, RSBSBL has tremendous potential for channel selection in P300 tasks.

A scalable quasi-Newton estimation algorithm for dynamic generalised linear models

ABSTRACT This research develops a scalable computing method based on quasi-Newton algorithm for several estimation problems in dynamic generalised linear models (DGLMs). The new method is developed by applying the principle of maximising a pointwise penalised quasi-likelihood (PPQ) for a DGLM for observed data often of massive size. Statistical and computational challenges involved in this development have been effectively tackled by exploiting the specific block structure and sparsity involved in the underlying projection matrix. The obtained maximum PPQ estimator of the state vector in the DGLM has been shown to be consistent and asymptotically normal under regularity conditions. Numerical studies and real data applications are conducted to assess the performance of the developed method.

Particle number conservation and block structures in matrix product states

The eigenvectors of the particle number operator in second quantization are characterized by the block sparsity of their matrix product state representations. This is shown to generalize to other classes of operators. Imposing block sparsity yields a scheme for conserving the particle number that is commonly used in applications in physics. Operations on such block structures, their rank truncation, and implications for numerical algorithms are discussed. Explicit and rank-reduced matrix product operator representations of one- and two-particle operators are constructed that operate only on the non-zero blocks of matrix product states.

Compression Reconstruction and Fault Diagnosis of Diesel Engine Vibration Signal Based on Optimizing Block Sparse Bayesian Learning.

It is critical to deploy wireless data transmission technologies remotely, in real-time, to monitor the health state of diesel engines dynamically. The usual approach to data compression is to collect data first, then compress it; however, we cannot ensure the correctness and efficiency of the data. Based on sparse Bayesian optimization block learning, this research provides a method for compression reconstruction and fault diagnostics of diesel engine vibration data. This method’s essential contribution is combining compressive sensing technology with fault diagnosis. To achieve a better diagnosis effect, we can effectively improve the wireless transmission efficiency of the vibration signal. First, the dictionary is dynamically updated by learning the dictionary using singular value decomposition to produce the ideal sparse form. Second, a block sparse Bayesian learning boundary optimization approach is utilized to recover structured non-sparse signals rapidly. A detailed assessment index of the data compression effect is created. Finally, the experimental findings reveal that the approach provided in this study outperforms standard compression methods in terms of compression efficiency and accuracy and its ability to produce the desired fault diagnostic effect, proving the usefulness of the proposed method.

A Block Sparse-Based Dynamic Compressed Sensing Channel Estimator for Underwater Acoustic Communication

Due to the complex ocean propagation environments, the underwater acoustic (UWA) multipath channel often exhibits block sparse time-varying features, and while dynamic compressed sensing (DCS) can mitigate the time-varying effects of the UWA channel, DCS-based algorithms have limited performance for the UWA channel with block sparsity. In this study, by formulating the UWA channel with blocks concatenation, a block sparse-based DCS approach (BS-CS) is proposed to explore the block and time-varying sparsity of UWA channel simultaneously. In detail, we firstly adopt a block sparse recovery algorithm, block orthogonal matching pursuit (BOMP), to compute the temporary estimate. Then, the CS approach is applied to compute the support additions, which are caused by the time-varying components of the UWA channel. Next, we use the selected support to perform the BOMP estimate, and obtain the estimated channel response. Finally, the numerical simulation and the sea experiment were carried out to verify the superior performance of the proposed BS-CS algorithm in the block sparse time-varying UWA channels.

Channel Estimation for Wideband mmWave MIMO OFDM System Exploiting Block Sparsity

In this letter, we investigate time-domain channel estimation for wideband millimeter wave (mmWave) MIMO OFDM system. By transmitting frequency-domain pilot symbols as well as different beamforming vectors, we observe that the time-domain mmWave MIMO channels exhibit channel delay sparsity and especially block sparsity among different spatial directions. Then we propose a time-domain channel estimation exploiting block sparsity (TDCEBS) scheme, which always aims at finding the best nonzero block achieving the largest projection of the residue at each iterations. In particular, we evaluate the system performance using the QuaDRiGa which is recommended by 5G New Radio to generate wideband mmWave MIMO channels. The effectiveness of the proposed TDCEBS scheme is verified by the simulation results, as the proposed scheme outperforms the existing schemes.

Grouping sparse filtering: a novel down-sampling approach toward rotating machine intelligent diagnosis in 1D-convolutional neural networks

Convolutional neural networks (CNNs) have weight-sharing and feature-learning abilities, and can efficiently and effectively be used for the health monitoring of industrial equipment. However, the pooling operation in a typical CNN can cause the loss of valuable impulse features during data down-sampling. We propose grouping sparse filtering (GSF) to overcome this problem. Instead of using a pooling operation, the GSF splits the channels of features obtained after convolution into equal-length groups. A feature selector with a feature aggregation function based on the channel importance factors and a lasso constraint is used to filter the groups to perform down-sampling. The GSF method preserves the impulse features due to the block sparsity of the vibration signal. Theoretical analysis demonstrates that the GSF has a similar computational complexity to using a pooling layer in a CNN for the same number of layers. Two experimental studies were conducted using data from a laboratory test and industrial environments. The experimental results show that the 1D-CNN with GSF provides better performance for retaining the impulse features of the rotating machinery signals and higher fault identification accuracy than a CNN with a pooling layer.

Application of Block Sparse Bayesian Learning in Power Quality Steady-State Data Compression

In modern power systems, condition monitoring equipment generates a great deal of steady-state data that are too large for data transmission and, thus, data compression is needed. Therefore, there is a balance to strike between compression quality and data accuracy. Greedy algorithms are effective but suffer from low data reconstruction accuracy. This paper proposes a block sparse Bayesian learning (BSBL)-based data compression method. Based on the prior distribution and posterior probability of the sparse signals, it uses the Bayesian formula to excavate the block structure of these signals. This paper also adds two indicators to the evaluation process to validate the proposed method. The proposed method is effective in terms of signal-to-noise ratio (SNR), relative root mean square error (RRMSE), amplitude error, energy recovery percentage (ERP), and angle error. The first three indicate better performance of the proposed method than the traditional method by giving the same compression ratio. Therefore, the method validates the possibility of a more accurate and economical solution to power quality assurance.

Fast Burst-Sparsity Learning-Based Baseline Correction (FBSL-BC) Algorithm for Signals of Analytical Instruments.

Baseline correction is a critical step for eliminating the interference of baseline drift in spectroscopic analysis. The recently proposed sparse Bayesian learning (SBL)-based method can significantly improve the baseline correction performance. However, it has at least two disadvantages: (i) it works poorly for large-scale datasets and (ii) it completely ignores the burst-sparsity structure of the sparse representation of the pure spectrum. In this paper, we present a new fast burst-sparsity learning method for baseline correction to overcome these shortcomings. The first novelty of the proposed method is to jointly adopt a down-sampling strategy and construct a multiple measurements block-sparse recovery problem with the down-sampling sequences. The down-sampling strategy can significantly reduce the dimension of the spectrum; while jointly exploiting the block sparsity among the down-sampling sequences avoids losing the information contained in the original spectrum. The second novelty of the proposed method is introducing the pattern-coupled prior into the SBL framework to characterize the inherent burst-sparsity in the sparse representation of spectrum. As illustrated in the paper, burst-sparsity commonly occurs in peak zones with more denser nonzero coefficients. Properly utilizing such burst-sparsity can further enhance the baseline correction performance. Results on both simulated and real datasets (such as FT-IR, Raman spectrum, and chromatography) verify the substantial improvement, in terms of estimation accuracy and computational complexity.

Guest editorial: Smart communications and networking: architecture, applications, and future challenges

Guest editorial: Smart communications and networking: architecture, applications, and future challenges

Generalized residual ratio thresholding

Recovering sparse high dimensional vectors from low dimensional linear measurements is an important compressive sensing (CS) problem. Many CS algorithms assume a priori knowledge of parameters like signal sparsity or noise variance which are unavailable in most real-life problems. It is also difficult to efficiently estimate these parameters with finite sample guarantees. This article proposes a support recovery technique called generalized residual ratio thresholding (GRRT) that can operate many popular sparsity or noise variance dependent sparse recovery algorithms in a sparsity and noise variance oblivious fashion with finite sample guarantees when the noise is composed of independent and identically distributed (i.i.d) Gaussian random variables and design matrix satisfies certain regularity conditions. Numerical simulations and theoretical results in sparse estimation scenarios like single measurement vector, multiple measurement vectors, block sparsity etc. indicate that the performance of algorithms operated using GRRT is comparable to the performance of same algorithms when operated with a priori knowledge of sparsity and noise variance.

Centralized and Decentralized Active User Detection and Channel Estimation in mMTC

We consider the problem of estimating channel and detecting active users in the uplink of a massive machine type communication (mMTC) network. We propose a centralized coupled prior based sparse Bayesian learning (cCP-SBL) algorithm that exploits the sporadic user activity and variable-sized block mMTC channel sparsity in the virtual angular domain. To achieve this objective, we first design a generalized coupled hierarchical Gaussian prior which captures this variable-sized block sparsity. We then derive its sub-optimal precision hyperparameter updates using majorization minimization framework. We next design a decentralized CP-SBL (dCP-SBL) algorithm for the emerging base station architectures with multiple processing units. The dCP-SBL algorithm converts the centralized hyperparameter cCP-SBL updates to an equivalent optimization problem, and solves it decentrally using asynchronous alternating direction method of multipliers. We also theoretically analyze the convergence of the dCP-SBL algorithm. We show using extensive numerical investigations that the i) proposed cCP- and dCP-SBL algorithms outperform several existing state-of-the-art designs; and ii) dCP-SBL algorithm is robust to processing unit failures and has a lower time complexity than the cCP-SBL algorithm.

Compressed spectrum sensing for grant-free NOMA based internet of vehicles

With the development of communication technology, non-orthogonal multiple access (NOMA) technology is proposed to meet the requirements of high throughput and low latency in massive machine type communication (mMTC) of Internet of Vehicles (IoV). In grant-free NOMA based IoV, mMTC has the characteristics of sparse active users at the same time, which makes the detection and recovery of user information critical. In this paper, considering the sparsity of active users in mMTC, we present a new block sparsity method under compressed sensing model that enables us to detect activity of users and recover user information with high accuracy and low complexity. The recovered algorithm used in our study is known as block sparse ISD algorithm, which exploits block sparse structure based on the ISD algorithm. The simulation results show that the proposed method is able to realize more performance gains in sparse signal recovery than traditional algorithm.

Off-Grid DOA Estimation With Mutual Coupling via Block Log-Sum Minimization and Iterative Gradient Descent

Mutual coupling (MC) effect between antennas can deteriorate the direction of arrival (DOA) estimation performance. Block sparse signal representation (BSSR) is an effective solution to mitigate the MC effect. Nevertheless, continuous angle space has to be discretized into a finite set of grid points, which lead to the grid mismatch. In this paper, we present an iterative block sparsity reconstruction algorithm for off-grid DOA estimation with MC. First, by exploiting the banded symmetric Toeplitz structure of MC matrix, a reduced BSSR model is formulated to preferably mitigate the MC effect. Then, an iterative block sparsity reconstruction algorithm with multiple measurement vectors (MMV) is proposed. Due to the NP-hard property of block l0 norm minimization, a block log-sum minimization method is developed to encourage sparsity for such a block sparse recovery problem, and a surrogate objective function is derived via the majorization-minimization approach. Finally, an iterative gradient descent algorithm is explored to refine the DOAs. Simulations verify that the proposed off-grid algorithm has robustness under limited snapshots and coherent sources.

Efficient energy-based orthogonal matching pursuit algorithm for multiple sound source localization with unknown source count

In this paper, we propose a compressed sensing (CS) sound source localization algorithm based on signal energy to solve the problem of stopping the iteration condition of the orthogonal matching pursuit (OMP) reconstruction algorithm in CS. The orthogonal matching tracking algorithm needs to stop iteration according to the number of sound sources or the change of residual. Generally, the number of sound sources cannot be known in advance, and the residual often leads to unnecessary calculation. Because the sound source is sparsely distributed in space, and its energy is concentrated and higher than that of the environmental noise, the comparison of the signal energy at different positions in each iteration reconstruction signal is used to determine whether the new sound source is added in this iteration. At the same time, the block sparsity is introduced by using multiple frequency points to avoid the problem of different iteration times for different frequency points in the same frame caused by the uneven energy distribution in the signal frequency domain. Simulation and experimental results show that the proposed algorithm retains the advantages of the orthogonal matching tracking sound source localization algorithm, and can complete the iteration well. Under the premise of not knowing the number of sound sources, the maximum error between the number of iterations and the set number of sound sources is 0.31. The experimental results show that the proposed algorithm has good positioning accuracy and has certain anti-reverberation capability. Compared with other OMP algorithms, the proposed algorithm has better iterative ability and stability. This work is helpful in promoting the development of multiple sound source localization.

Robust Proportionate Normalized Least Mean M-Estimate Algorithm for Block-Sparse System Identification

In practical applications, the impulse responses (IRs) of some network echo paths are blocksparse (BS), while the traditional proportionate and zero attraction algorithms do not consider the prior sparsity of the BS system, so they do not perform well in the block-sparse system identification (BSSI). In addition, most of the current BS filtering algorithms are based on the assumption of Gaussian noise, so the performance will deteriorate seriously in the background of impulse noise. To overcome the shortcoming, we use the mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2,1} $ </tex-math></inline-formula> norm of the filter weight vector to fully tap the sparsity of the BS system, and combine the anti impulse noise characteristic of the M-estimate function to design and derive the BS proportionate normalized least mean M-estimate (BSPNLMM) algorithm from the perspective of basis pursuit (BP), which well realizes the BSSI in the presence of impulse noise. Then, we analyze the mean performance of the BSPNLMM algorithm in detail and give the stable step size bound. Finally, the superiority of the proposed BSPNLMM algorithm is verified by numerical simulations

Recovery Conditions of Sparse Signals Using Orthogonal Least Squares-Type Algorithms

Orthogonal least squares (OLS)-type algorithms are efficient in reconstructing sparse signals, which include the well-known OLS, multiple OLS (MOLS) and block OLS (BOLS). In this paper, we first investigate the noiseless exact recovery conditions of these algorithms. Specifically, based on mutual incoherence property (MIP), we provide theoretical analysis of OLS and MOLS to ensure that the correct nonzero support can be selected during the iterative procedure. Nevertheless, theoretical analysis for BOLS utilizes the block-MIP to deal with the block sparsity. Furthermore, the noiseless MIP-based analyses are extended to the noisy scenario. Our results indicate that for K-sparse signals, when MIP or SNR satisfies certain conditions, OLS and MOLS obtain reliable reconstruction in at most K iterations, while BOLS succeeds in at most (K/d) iterations where d is the block length. It is shown that our derived theoretical results improve the existing ones, which are verified by simulation tests.

Multi-Frame Constrained Block Sparse Bayesian Learning for Flexible Tactile Sensing Using Electrical Impedance Tomography

In this paper, we presented a multi-frame constrained block sparse Bayesian learning (MFC-BSBL) reconstruction algorithm to tackle the challenge of poor-quality reconstruction images in electrical impedance tomography (EIT) for tactile sensing. The fundamental idea of MFC-BSBL is to explore the sparsity, intra-frame correlation, and inter-frame correlation of impedance distributions by extending the Bayesian inference framework. To verify the proposed algorithm, we conducted numerical simulations for different cases to identify one, multiple, round, and square targets. The simulation results demonstrated that this method can effectively detect the target positions and shapes by reducing artifacts and noise in the reconstructed images. To demonstrate the application of this approach to real EIT-based tactile sensing, we conducted real-contact detection experiments using the EIT tactile sensor system. Compared with traditional methods, the tactile sensor system using the MFC-BSBL algorithm can achieve accurate contact detection and significantly reduce artifacts and noise.

Low pilot overhead channel estimation for CP‐OFDM‐based massive MIMO OTFS system

In high-speed mobile scenarios, due to the high-speed relative motion between transmitter and receiver, the high Doppler frequency shift interferes with the inter-subcarrier orthogonality in orthogonal frequency-division multiplexing (OFDM) systems. Therefore its performance is significantly degraded. Recently, orthogonal time–frequency space (OTFS) is considered as an effective alternative scheme to OFDM for time-varying channels. As with OFDM-massive multiple input multiple output (MIMO) systems, downlink channel estimation is necessary for OTFS-massive MIMO systems to improve the spectral efficiency in frequency-division duplex (FDD) mode without channel reciprocity. Here, first the cyclic prefix -OFDM-based massive MIMO OTFS system channel with antenna directivity pattern is analyzed, and transform the burst sparsity in the angle domain into block sparsity by using non-uniform Fourier transform (NUFT). Furthermore, to solve the problem that the pilot overhead grows linearly with the number of antennas, we propose a three-dimensional (3D) dynamic support detect (DSD) algorithm. Compared with the traditional OMP algorithm, and the 3D-structured orthogonal matching pursuit algorithm, simulation results demonstrate the proposed DSD algorithm has higher channel estimation accuracy, and lower pilot overhead.