Sparse Signal Representation Research Articles

Blade tip timing signals parameters identification based on Displacement Offset Decreased and Compressed Sensing

High-speed rotating blade vibration monitoring is of great significance for the safe operation of turbomachinery. Blade Tip Timing (BTT) is considered a promising technology in the field of blade vibration monitoring. The BTT signal analysis has the following problem, the displacement offset was caused by speed variation which affected the accuracy of the blade vibration parameter identification. Owing to the under-sampled characteristics of the BTT signals and multiple sensor data are required to identify the parameters. The accurate extraction of blade vibration characteristics is challenging. Thus, a vibration analysis method is proposed based on Displacement Offset Decreased and Compressed Sensing (DOD-CS). Firstly, the BTT signal pairwise is subtracted to reduce the impact of the displacement offset, and based on the subtractive results, a basis function is constructed to rebuild the dictionary matrix of the compressed sensing method. Then, we solved the signal sparse representation equation and obtained the spectrum estimation result, that is, the structure vibration parameters. The analysis of simulation data shows that the parameter identification accuracy of the DOD-CS method is higher than that of the OMP-CS (Orthogonal Matching Pursuit and Compressed Sensing) method, and the identification errors of frequency and amplitude are within 1% and 5%, respectively. The experimental results confirm the feasibility of the proposed method in identifying vibration parameters. Compared with existing methods, the innovation of the proposed method is that it eliminates the influence of displacement offset on the accuracy of parameter identification. For under-sampled signals, only two sensor data information are needed to complete spectrum estimation and parameter identification.

A dictionary learning based unsupervised neural network for single image compressed sensing

In the field of Compressed Sensing (CS), the sparse representation of signals and the advancement of reconstruction algorithms are two critical challenges. However, conventional CS algorithms often fail to sufficiently exploit the structured sparsity present in images and suffer from poor reconstruction quality. Most deep learning-based CS methods are typically trained on large-scale datasets. Obtaining a sufficient number of training sets is challenging in many practical applications and there may be no training sets available at all in some cases. In this paper, a novel deep Dictionary Learning (DL) based unsupervised neural network for single image CS (dubbed DL-CSNet) is proposed. It is an effective trainless neural network that consists of three components and their corresponding loss functions: 1) a DL layer that consists of multi-layer perceptron (MLP) and convolution neural networks (CNN) for latent sparse features extraction with the L1-norm sparsity loss function; 2) an image smoothing layer with the Total Variation (TV) like image smoothing loss function; and 3) a CS acquisition layer for image compression, with the Mean Square Error (MSE) loss function between the original image compression and the reconstructed image compression. In particular, the proposed DL-CSNet is a lightweight and fast model that does not require datasets for training and exhibits a fast convergence speed, making it suitable for deployment in resource-constrained environments. Experiments have demonstrated that the proposed DL-CSNet achieves superior performance compared to traditional CS methods and other unsupervised state-of-the-art deep learning-based CS methods.

Multi-angle speed-of-sound imaging with sparse sampling to characterize medical tissue properties

Medical Speed-of-sound (SoS) imaging, which can characterize medical tissue properties better by quantifying their different SoS, is an effective imaging method compared with conventional B-mode ultrasound imaging. As a commonly used diagnostic instrument, a hand-held array probe features convenient and quick inspection. However, artifacts will occur in the single-angle SoS imaging, resulting in indistinguishable tissue boundaries. In order to build a high-quality SoS image, a number of raw data are needed, which will bring difficulties to data storage and processing. Compressed sensing (CS) theory offers theoretical support to the feasibility that a sparse signal can be rebuilt with random but less sampling data. In this study, we proposed an SoS reconstruction method based on CS theory to process signals obtained from a hand-held linear array probe with a passive reflector positioned on the opposite side. The SoS reconstruction method consists of three parts. Firstly, a sparse transform basis is selected appropriately for a sparse representation of the original signal. Then, considering the mathematical principles of SoS imaging, the ray-length matrix is used as a sparse measurement matrix to observe the original signal, which represents the length of the acoustic propagation path. Finally, the orthogonal matching pursuit algorithm is introduced for image reconstruction. The experimental result of the phantom proves that SoS imaging can clearly distinguish tissues that show similar echogenicity in B-mode ultrasound imaging. The simulation and experimental results show that our proposed method holds promising potential for reconstructing precision SoS images with fewer signal samplings, transmission, and storage.

Stress Wave Hybrid Imaging for Detecting Wood Internal Defects under Sparse Signals

Stress wave technology is very suitable for detecting internal defects of standing trees, logs, and wood and has gradually become the mainstream technology in this research field. Usually, 12 sensors are positioned equidistantly around the cross-section of tree trunks in order to obtain enough stress wave signals. However, the arrangement of sensors is time-consuming and laborious, and maintaining the accuracy of stress wave imaging under sparse signals is a challenging problem. In this paper, a novel stress wave hybrid imaging method based on compressive sensing and elliptic interpolation is proposed. The spatial structure of the defective area is reconstructed by using the advantages of compressive sensing in sparse signal representation and solution of stress waves, and the healthy area is reconstructed by using the elliptic space interpolation method. Then, feature points are selected and mixed for imaging. The comparative experimental results show that the overall imaging accuracy of the proposed method reaches 89.7%, and the high-quality imaging effect can be guaranteed when the number of sensors is reduced to 10, 8, or even 6.

Sparse Ramanujan Sequences Transform based OFDM for PAPR Reduction

Sparse Ramanujan Sequences (SRS) are periodic series derived from Ramanujan Sums (RS). RS is an exponential summation used to derive infinite series expansions for arithmetic functions, whose application pervades different fields of study from classical mathematics to digital signal processing. SRS has properties similar to RS such as periodicity and orthogonality. SRS transforms allow the sparse representation of signals, hence they have many potential applications, such as denoising and compression. The application of SRS transform to reduce the Peak to Average Power Ratio (PAPR) in Orthogonal Frequency Division Multiplexing (OFDM) is proposed in this paper. The Complementary Cumulative Distribution Function (CCDF) and Bit Error Rate (BER) are used to assess the PAPR reduction performance of the proposed system. The results show that the proposed SRS transform-based OFDM system significantly reduces PAPR and BER with reduced computational complexity in comparison with the existing systems.

Failure Mode Classification for Rolling Element Bearings Using Time-Domain Transformer-Based Encoder.

In this paper, we propose a Transformer-based encoder architecture integrated with an unsupervised denoising method to learn meaningful and sparse representations of vibration signals without the need for data transformation or pre-trained data. Existing Transformer models often require transformed data or extensive computational resources, limiting their practical adoption. We propose a simple yet competitive modification of the Transformer model, integrating a trainable noise reduction method specifically tailored for failure mode classification using vibration data directly in the time domain without converting them into other domains or images. Furthermore, we present the key architectural components and algorithms underlying our model, emphasizing interpretability and trustworthiness. Our model is trained and validated using two benchmark datasets: the IMS dataset (four failure modes) and the CWRU dataset (four and ten failure modes). Notably, our model performs competitively, especially when using an unbalanced test set and a lightweight architecture.

Multiplicative Basis Function Based Adaptive DOA Estimation in Optimal MIMO Sparse Antenna Reconfiguration Model

Direction of arrival (DOA) estimation using sparse signal representation has gained significant attention in recent decades. The spatial signals utilized for DOA estimation are reconstructed through a novel compressive sensing (CS) approach. In this study, we used a CS approach to ascertain the adaptive underdetermined DOA for multiple inputs and multiple output (MIMO) sparse media. Accurate DOA estimation through the CS approach contributes to enhanced signal investigation and the suppression of undesired noise in a sparse channel. The method proposed herein encompasses the development and execution of a novel multiplicative basis function known as the multi-kernel supported non-negative sparse Bayesian learning (NNSBL) algorithm, which is implemented on predefined grid values. Concurrently, stochastic grey wolf optimization (GWO) is virtually applied to increase the degrees of freedom (DOF) on a minimum redundancy array (MRA) while considering an optimal antenna reconfiguration model. The advantages of this proposed approach include the generation of a distinct manifold matrix for precise beam steering, resulting in improved DOA estimation accuracy. Additionally, an augmentation of DOF using GWO was observed, with low computational complexity. The simulated result of proposed algorithm leads to the attainment of optimal minimum root mean square error (RMSE) across various optimal wavelengths of the stochastic sources. Finally, a comparative analysis of RMSE and convergence plots confirms the superior performance and high potentiality of the proposed method in comparison to existing techniques across different SNR values. Notably, there is significant reduction in RMSE which is suitable for precise DOA estimation in signal processing applications.

Prestack sparse envelope seismic inversion method adopting the L0−L2-norm regularization

The high drilling costs limit the possibility of obtaining reliable low-frequency constrained models in marine environments or areas with sparse well-log data, making it difficult to constrain lateral continuity and deep data. To enhance stability and accuracy in prestack seismic inversion in these areas, an elastic parameter estimation approach using sparse envelope inversion with [Formula: see text]-norm regularization is proposed. The method combines signal sparse representation and modulation theories to derive a new formula for sparse envelope extraction at lower frequencies. By applying [Formula: see text]-norm regularization to the sparse envelope, we obtain parameter inversion results with smoothed trends, augmenting low-wavenumber information for improved model constraints. In addition, taking the envelope inversion results obtained by the [Formula: see text] norm as the model constraint, the sparsest inversion results with obvious block-like characteristics are obtained by regularizing the inversion equation with the [Formula: see text] norm. Notably, the new method effectively suppresses wavelet side lobes, resulting in stable and accurate inversions without the need for initial low-frequency models. A synthetic example is used to illustrate the feasibility and stability of proposed approach and further demonstrate its practicality in reservoir parameter estimation through a field case study of gas exploration.

Dictionary learning with cone atoms and application to anomaly detection

We propose a variant of dictionary learning (DL) for sparse representations where the atoms are cones instead of simple vectors. The most convenient vector from a cone, called actual atom, is used to build the linear sparse representation of a given signal. We present a DL algorithm suited for cone atoms, which can update the dictionary without storing all the actual atoms that are used in the representations of the training signals. Also, the algorithm ensures that the cone atoms are disjoint and thus the representation problem is well posed. We use the proposed cone DL for anomaly detection. On a specific type of anomaly, called “dependency”, the DL methods involving cone atoms are better than those from a reputed benchmark. They are also better than standard DL.

Elliptic tangent imaging method for layered plate interfacial defects based on non-dispersive guided waves

Layered structures play an increasingly pivotal role in diverse fields such as aerospace, pipeline transportation, and petrochemical engineering. However, defects situated at the interfaces between layers pose a challenge for conventional Non-Destructive testing (NDT) methods, impeding accurate imaging. This research introduces the elliptic tangent imaging method based on interface wave modes to visualize interfacial defects within layered structures. The interface wave mode, characterized by high-frequency non-dispersive traits, facilitates precise localization of defects. Its energy concentration in the interface enhances sensitivity to interfacial defects. The elliptic tangent imaging method proposed in this paper capitalizes on the transmission coefficients of the oblique incidence technique for surface waves, enabling the concurrent determination of defect location and orientation using one pair of transducers. The application of the orthogonal matched pursuit algorithm for sparse representation of the raw signal further enhances positioning accuracy. This paper establishes an automatic detection system for interface waves, demonstrating swift transducer switching. Experimental validation of wave velocity aligns closely with theoretical calculations. In experiments focusing on interfacial defect imaging in bilayer aluminum-steel plates, the system exhibits the capability to accurately depict interfacial defects with varying orientations.

DOA estimation of coherent signals in underdetermined problems using sparse-based Toeplitz covariance reconstruction

Direction-Of-Arrival (DOA) estimation in environments with coherent sources is a challenging problem, when the number of narrowband sources is more than elements and current coherent algorithms cannot accurately overcome such underdetermined problems. In this paper, we propose the Sparse-based Toeplitz Covariance Reconstruction (STCR) algorithm, which obtains a hole-free extended-aperture array with increased Degrees of Freedom (DOF) by exploiting a minimum redundancy array. This method provides superiority in estimating coherent sources by Toeplitz covariance matrix reconstruction. Also, using a Sparse Signal Representation (SSR) framework makes the DOA estimator stronger in source detection and robust to the noise power. Numerical results show the effectiveness of the proposed method even at low SNRs for over- and underdetermined DOA estimators compared to well-known methods. Also, it has high accuracy in DOA estimation of closely-located coherent sources using a small number of snapshots.

The A*orthogonal least square algorithm with the self-training dictionary for propeller signals reconstruction

The transmission of huge propeller signals via underwater wireless networks has high energy consumption, and conventional compression methods based on Nyquist sampling theorem cannot achieve efficient compression. Different from conventional compression methods, compressed sensing (CS) realizes the sub-Nyquist sampling rate, but the sparse signal is one of the preconditions of CS. Unfortunately, propeller signals are always non-sparse in both time and frequency domains. Therefore, the commonly used fixed dictionary is not suitable for sparse representation of propeller signals. To improve sparse representation, this paper proposes a self-training dictionary (STD) scheme, which updates the dictionary and sparse encoding simultaneously in iterations. Combining with the STD scheme, a CS reconstruction based on A*orthogonal least square (A*OLS) is proposed. In detail, a candidate subset selected by the orthogonal least square (OLS) algorithm is used as the node of the tree, and the search tree is established by A*search to find the optimal sparse solution. The experimental results confirm that the STD-A*OLS framework has significant advantages in performance including recovered signal-to-noise ratio (RSNR), percent norm difference (PND), and structure similarity index measure (SSIM).

A fast threshold OMP based on self-learning dictionary for propeller signal reconstruction

The acquisition of propeller signals can be applied to localization and fault diagnosis, etc. However, recording a large amount of propeller signals results in higher costs. Compressive sensing (CS) is an effective approach to processing large data. CS algorithms work well for sparse signals, but propeller signals are non-sparse in both the time and frequency domains. Therefore, the traditional fixed dictionary, such as discrete cosine transform (DCT), has a limited sparse representation of propeller signals. We propose a self-learning dictionary in this study, the self-learning dictionary uses the propeller signal as input to train the dictionary, and the trained dictionary can be stored and used for sparse representation of propeller signals. Based on the self-learning dictionary, we propose a threshold orthogonal matching pursuit based on QR decomposition (TOMP-QR) algorithm. We use the ratio of two energy thresholds as the stopping condition of the TOMP-QR algorithm, which is more robust under arbitrary noise. Then, we use QR decomposition to reduce the complexity of the algorithm. The simulation results verify the effectiveness of the proposed method in signal reconstruction accuracy and running time. Based on DCT, discrete wavelet transform (DWT) and self-learning dictionary, we compare the TOMP-QR algorithm with TOMP, OMP, sparsity adaptive matching pursuit (SAMP) and stage wise OMP (StOMP) algorithm to reconstruct propeller signals in the experiment, the results show that the effectiveness and superiority of the self-learning dictionary and TOMP-QR algorithm.

Pulsation artifact removal from intra-operatively recorded local field potentials using sparse signal processing and data-specific dictionary.

Neural recordings frequently get contaminated by ECG or pulsation artifacts. These large amplitude components can mask the neural patterns of interest and make the visual inspection process difficult. The current study describes a sparse signal representation strategy that targets to denoise pulsation artifacts in local field potentials (LFPs) recorded intraoperatively. To estimate the morphology of the artifact, we first detect the QRS-peaks from the simultaneously recorded ECG trace as an anchor point. After the LFP data has been epoched with respect to each beat, a pool of raw data segments of a specific length is generated. Using the K-singular value decomposition (K-SVD) algorithm, we constructed a data-specific dictionary to represent each contaminated LFP epoch in a sparse fashion. Since LFP is aligned to each QRS complex and the background neural activity is uncorrelated to the anchor points, we assumed that constructed dictionary will be formed to mainly represent the pulsation artifact. In this scheme, we performed an orthogonal matching pursuit to represent each LFP epoch as a linear combination of the dictionary atoms. The denoised LFP data is thus obtained by calculating the residual between the raw LFP and its approximation. We discuss and demonstrate the improvements in denoised data and compare the results with respect to principal component analysis (PCA). We noted that there is a comparable change in the signal for visual inspection to observe various oscillating patterns in the alpha and beta bands. We also see a noticeable compression of signal strength in the lower frequency band (<13 Hz), which was masked by the pulsation artifact, and a strong increase in the signal-to-noise ratio (SNR) in the denoised data.Clinical Relevance- Pulsation artifact can mask relevant neural activity patterns and make their visual inspection difficult. Using sparse signal representation, we established a new approach to reconstruct the quasiperiodic pulsation template and computed the residue signal to achieve noise-free neural activity.

A novel method to repair missing vibration data in rolling bearing vibration signals based on improved optimized measurement matrix

Missing data, caused by many factors such as equipment short circuits or data cleaning, affect the accuracy of condition monitoring for rotating machinery. To improve the precision of missing data recovery, a compressed sensing-based vibration data repair method is developed. First, based on the Gaussian random matrix, an improved optimized measurement matrix (OMM) is proposed to accurately sample data. Then, a sparse representation of the vibration signal, through a discrete cosine transform, is utilized to make the noisy vibration signal sparse. Finally, the orthogonal matching pursuit algorithm is employed to reconstruct the missing signal. The effectiveness of the proposed method is verified by analyzing constant and variable speed time series of rolling bearings. Compared with other data repair methods, it is shown that the OMM has a higher repair precision at different loss rates.

Intelligent Detection to Laser Welding Seam Defect Using Adaptive Joint Wavelet Dictionary Learning of PEC Signal

Abstract The pulsed eddy current (PEC) is an effective method for the online detection of laser welding seam defects. The joint wavelet dictionary learning method is proposed for solving the separation problem of the broad frequency harmonic and local non-smooth distortion of the PEC signal. The Haar and Gabor wavelet is adopted to be the basic function, which is extended to be the over complete wavelet dictionary library by cyclic migration. The sparse representation of the defect PEC signal is obtained by combining the joint wavelet dictionary with the orthogonal matching pursuit algorithm. The feature parameters of the PEC signal are calculated and inputted into the support vector machine to detect the laser welding seam defect intelligently. The validity of the proposed method is further verified by the experimental results, demonstrating the effectiveness of the classification identification and quantitative assessment of the pore and crack.

A 2D prediction step using multiquadric local interpolation with adaptive parameter estimation for image compression

We present and analyze several prediction strategies in the 2D setting based on multiquadric radial basis function interpolation with either linear or Weighted Essentially Non Oscillatory (WENO) shape parameter approximation. When considered within Harten’s framework for Multiresolution, these prediction operators give rise to sparse multi-scale representations of 2D signals, whose compression capabilities are demonstrated through numerical experiments. It is well know that the accuracy of multiquadric interpolation depends on the choice of the shape parameter. In addition, in [6], it was shown that the use of data-dependent strategies in the selection of the shape parameter leads to more accurate reconstructions. We shall show that our local adaptive estimates of the shape parameters lead to non-separable, fully 2D, reconstruction strategies that lead, in turn, to efficient compression algorithms.

Compressed sampling of gearbox oil temperature signal based on an improved intrinsic mode function basis mixed-dictionary

The oil temperature signal of gearbox is always redundant in long-term use, which will occupy a lot of computer storage space. An improved intrinsic mode function basis mixed-dictionary K-singular value decomposition (IMDK-SVD) algorithm for compressed sampling of the aperiodic oil temperature signal is proposed. Firstly, an improved mixed-dictionary is designed for sparse representation of the aperiodic oil temperature signal, this mixed-dictionary is composed of a class-specific dictionary that extracts the commonness of the same group of data and a shared dictionary that extracts the difference of the different group of data. Secondly, the measurement matrix with variable-step sampling is proposed, and the sampling points is adaptively determined by the information entropy index of signal. Benefitting from these improvements, the advantages of high reconstruction accuracy and saving sampling points as possible are achieved, and the effectiveness of proposed method is verified based on the simulation signal and the experimental signal.

Sparse representation of acoustic emission signals and its application in pipeline leak location

The acoustic detection of pipeline leaks is strongly influenced by the associated interference and noise. In this paper, acoustic emission signals are analyzed using a sparse representation method and the main components associated with the leakage are extracted. Dictionary learning is performed using training samples composed of the leakage signals and noise signals. The measured signal is sparsely decomposed on the composite dictionary, allowing the main leakage components to be estimated. The effects of dictionary dimensionality, redundancy, sparsity constraints, and other parameters on the performance of the sparse representation algorithm are investigated. Finally, the leak location in the pipeline is determined through cross-correlation analysis of the reconstructed acoustic signals. Experimental results show that the proposed sparse representation method effectively improves the signal-to-noise ratio of the acoustic emission signals, and correspondingly improves the accuracy and reliability of pipeline leak location compared with traditional localization methods.

Partial discharge signal compression reconstruction method based on transfer sparse representation and dual residual ratio threshold

AbstractPartial discharge (PD) signals have a large amount of data and a low energy proportion of pulse signals, resulting in difficult data transmission and poor reconstruction efficiency. To this end, a PD signal compression reconstruction method based on transfer sparse representation and dual residual ratio threshold (TSR‐DRRT) is proposed. TSR‐DRRT is centred on the sparse representation (SR) and accurate reconstruction of noisy signals. The intrinsic pulse of PD signals is extracted by signal decomposition, and jointly trained with different types of signals to establish the transfer SR dictionary. The compressed signal accurately retains the essential characteristics of the pulse information by improving the match between the dictionary atoms and the polymorphic PD pulses. To match the transfer SR dictionary, the inner and outer DRRT iteration termination conditions are set adaptively during the reconstruction process based on the correlation difference between the dictionary and signal frames. Independent control of PD pulse recognition and reconstruction accuracy is achieved, and its performance under noisy signals is improved. The results show that the method can achieve high ratio compression and efficient reconstruction of noisy signals. Different types of PD signals can also have high matching accuracy. This method can meet the demand for PD signals compression and transmission to the terminal for accurate reconstruction.