Orthogonal Matching Pursuit Method Research Articles

Non-convex sparse regularization via convex optimization for blade tip timing

Blade Tip Timing (BTT), an emerging technology poised to replace strain gauges, enables contactless measurement of rotor blade vibration. However, the blade vibration signals measured by BTT systems often suffer from significant undersampling. Sparse reconstruction methods are instrumental in addressing the challenge of undersampled signal reconstruction. However, traditional approaches grounded in ℓ1 regularization tend to underestimate the amplitude of the true solution. This underestimation is particularly pronounced in the resonance state of the rotor blade, hindering effective prediction of the blade’s operational state. To overcome this limitation, this paper introduces a novel non-convex regularized BTT model, employing a non-convex penalty term with convex-preserving properties to achieve nearly unbiased reconstruction accuracy. Additionally, we propose a new threshold iteration algorithm designed for the swift solution of this model. The accuracy and robustness of the proposed method in identifying the multimodal vibration parameters of rotor blades are validated through simulations and experiments. Comparatively, the proposed method closely aligns with the Orthogonal Matching Pursuit (OMP) method in recognizing blade multimodal vibration amplitude, showcasing significant improvement over the ℓ1 regularization method. Furthermore, it demonstrates lower sensitivity to changes in BTT probe layout when compared to the OMP and ℓ1 regularization methods.

Confidence based compressed sensing approach with QoS differentiation for reliable grant-free access

With the rapid development of 5G technology, numerous intelligent terminals can be successively connected to a network. This brings significant challenges to existing network access because it increases the collision probability. It is essential for Grant-free random access (GF-RA) to ensure low delay and reliable transmission. Due to multiuser interference and varying environments, user detection can be complicated, which leads to unreliable transmission. To address the limitations above, research on the GF-RA method based on compressed sensing is carried out and it includes the following: (1) The confidence-weighted orthogonal matching pursuit method is used for estimating the number of active users and overcomes the constraint of sparse condition. (2) The confidence-weighted simultaneous hard thresholding (SHT) method is used for active user detection (AUD), which can improve the performance of the SHT algorithm. (3) We conduct collision probability analysis to not only provide the performance upper bound using the multiple preambles method but also infer the collision probability relationship with different priorities. This is helpful to realize diverse quality of service requirements. The numerical results prove that the proposed method is valid for non sparse signals and can realize a high success access rate.

Time analysis for aero-engine acoustic modes exploiting block sparsity

Acoustic mode analysis for aero-engines can offer valuable insights for the design of silent engines as well as for fault diagnosis. Commonly, this is done in the (spatial) Fourier domain, necessitating the use of multiple uniformly spaced microphones to ensure adequate resolution. Recent works show that sub-Nyquist estimation is feasible using sparse reconstruction frameworks, although such modelling generally introduces an estimation bias that has to be compensated for. Moreover, there is a growing interest in monitoring mode amplitude over continuous time, as it can offer crucial insights for diagnosing operational conditions. In this work, we introduce a Block Orthogonal Matching Pursuit (BOMP) method for continuous time mode analysis, exploiting the underlying structural sparsity of the signal model. Specifically, the (pseudo) ℓ0−norm penalty is employed to induce sparsity in the wavenumber domain, whereas a block structure is imposed as a constraint to monitor the amplitude variation in the time domain. The effectiveness of the BOMP is evaluated using both numerical simulations and experimental measurements, indicating the proposed method’s preferable performance as compared to the classic Least Absolute Shrinkage and Selection Operator (LASSO) and Orthogonal Matching Pursuit (OMP) methods.

A Modified OMP Method for Multi-Orbit Three Dimensional ISAR Imaging of the Space Target

The conventional two dimensional (2D) inverse synthetic aperture radar (ISAR) imaging fails to provide the targets' three dimensional (3D) information. In this paper, a 3D ISAR imaging method for the space target is proposed based on mutli-orbit observation data and an improved orthogonal matching pursuit (OMP) algorithm. Firstly, the 3D scattered field data is converted into a set of 2D matrix by stacking slices of the 3D data along the elevation direction dimension. Then, an improved OMP algorithm is applied to recover the space target's amplitude information via the 2D matrix data. Finally, scattering centers can be reconstructed with specific three dimensional locations. Numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed 3D imaging method.

Adaptive Non-Uniform Hybrid Beamforming for mmWave Train-to-Ground Communications in High-Speed Railway Scenarios

Higher frequency bands, especially millimeter wave (mmWave), are a key enabler for future high speed railway (HSR) wireless communication systems. Hybrid analog and digital beamforming (HBF) schemes operating at mmWave frequency bands can exploit the sparse nature of the channel by using large scale antenna arrays (LSAs) to shape multiple beams that overcome the severe path loss. However, due to the long and straight geometric characteristic of the rail track, there is a significant variance in the train-to-ground communication rate when the train is near or far from the BS. To address this issue, a novel hybrid beamforming scheme is developed based on a non-uniform beam design. We first model and investigate different beam design schemes in terms of spectral efficiency. Then, an efficient straight route based adaptively analog beamforming scheme with the non-uniform beam is proposed for HSR, which is designed to resist path loss. Finally, an adaptive non-uniform HBF algorithm based on the orthogonal matching pursuit method (OMP) is developed to minimize the rate gap between different locations by selecting the appropriate predefined beams. Numerical results show that the proposed hybrid beamforming scheme can efficiently ensure signal coverage, and reduce the variance of the train-to-ground communication rate along a straight track route.

A novel block compressive sensing algorithm for SAR image formation

Compressive Sensing (CS) theory has been used for Synthetic Aperture Radar (SAR) imaging due to the sparsity feature of SAR images. Therefore, some well-known CS algorithms like Orthogonal Matching Pursuit (OMP) and Regularized OMP (ROMP) methods have been employed for SAR image formation with a very small number of samples. On the other hand, it has been shown that the SAR signal is consistent with the definition of block sparsity. Hence, compressive sensing methods employing block structure, known as Block Compressive Sensing (BCS), are presented and used for SAR image formation to achieve more accuracy with a smaller number of samples. In this paper, first, a new BCS-based algorithm, namely, Block Norm Regularized Orthogonal Matching Pursuit (BNROMP), is introduced which can be used in all BCS applications. Then, this novel method is used for SAR image formation to achieve more accuracy and excellent resolution with a small number of samples. The simulation results for the synthesized data, as well as real data, show that by using the novel BNROMP method, we could form SAR images with higher quality, as compared to those for the standard image formation algorithms and other CS-SAR or BCS-SAR methods.

Copyright Protection of Music Multimedia Works Fused With Digital Audio Watermarking Algorithm

Copyright law is important in the media sector since an original creative work owner has the exclusive right to consent, publish, broadcast, and even translate or modify their work. A growing number of digital copyright issues can be found behind the widespread use of multimedia technologies. Improvements must be made right away to the copyright infringement prevention approach using digital watermarking. Zero-watermarking has lately gained popularity as one of the alternatives being considered. A novel sparse representation persistent-based digital audio watermarking algorithm (SRP-DAWA) has been presented to increase zero resilience. Using the improved singular value decomposition (iSVD) technique, an optimum over-complete dictionary can be generated from the background audio signal in the suggested method. Using the orthogonal matching pursuit (OMP) method, the sparse coefficient of a fragmented sample data is calculated, and the corresponding sparse matrix is generated.

Height Measurement for Meter Wave Polarimetric MIMO Radar with Electrically Long Dipole under Complex Terrain

Height measurement of meter wave radar is a difficult and important problem. This paper studies the height measurement of meter wave polarimetric (MWP)-MIMO array radar under complex terrain. The traditional electrically short dipole has low radiation efficiency, and the collocated dipole vector antenna has strong mutual coupling. This paper proposes to use electrically long dipoles and separated vector antennae to solve the problems of low radiation efficiency and strong mutual coupling. In addition, different from the traditional flat terrain, the research of this paper is based on the conditions of complex undulating terrain. First, the height measurement signal model of the MWP-MIMO radar with separated electrically long dipole under the complex terrain is derived. Then, a preprocessing method of block orthogonal matching pursuit is proposed to obtain the coarse estimation of the target’s elevation. Then, under the guidance of the coarse estimation, the generalized MUSIC algorithm is used to obtain the high-precision elevation estimation of the target, and then the height measurement of the target is obtained according to the geometric relationship. Finally, the effectiveness of the proposed algorithm is proved by computer simulations.

An improved orthogonal matching pursuit method for denoising high-frequency ultrasonic detection signals of flip chips

Noise suppression of an echo signal plays an important role in high-frequency ultrasonic testing of flip chips. This paper proposes an orthogonal matching pursuit (OMP) method optimized by an improved artificial bee colony (ABC) algorithm for denoising high-frequency ultrasonic testing signals of flip chips. We add adaptive learning factors to change the way the ABC randomly selects the search direction, which speeds up the convergence speed of the algorithm. The improved ABC, named adaptive artificial bee colony (AABC), replaces the greedy search process of OMP. Instead of searching for the atom that best matches the echo signal, the improved OMP algorithm searches for the optimal parameter and replaces the atom with a set of parameters with practical physical significance. The introduction of the AABC changes the search space of OMP from discrete dictionary space to continuous parameter space, which minimizes the error between the atom and echo signal and leads to an accurate approximation. Additionally, the AABC reduces the search times of OMP and improves the convergence speed. Then, the wavelet transform thresholding technology is combined with the attenuation characteristic of high-frequency ultrasound to eliminate the influence of error decomposition caused by noise and inaccurate sparsity setting. We present the noise suppression experimental results of high-frequency ultrasonic simulation and real testing signals of flip chips, including Gaussian white noise and correlated noise, and compare the proposed method with other sparse representation methods, including matching pursuit (MP) and OMP. The results demonstrate the superior performance of the proposed method.

Machine learning-enabled MIMO-FBMC communication channel parameter estimation in IIoT: A distributed CS approach

Compressed Sensing (CS) is a Machine Learning (ML) method, which can be regarded as a single-layer unsupervised learning method. It mainly emphasizes the sparsity of the model. In this paper, we study an ML-based CS Channel Estimation (CE) method for wireless communications, which plays an important role in Industrial Internet of Things (IIoT) applications. For the sparse correlation between channels in Multiple Input Multiple Output Filter Bank MultiCarrier with Offset Quadrature Amplitude Modulation (MIMO-FBMC/OQAM) systems, a Distributed Compressed Sensing (DCS)-based CE approach is studied. A distributed sparse adaptive weak selection threshold method is proposed for CE. Firstly, the correlation between MIMO channels is utilized to represent a joint sparse model, and CE is transformed into a joint sparse signal reconstruction problem. Then, the number of correlation atoms for inner product operation is optimized by weak selection threshold, and sparse signal reconstruction is realized by sparse adaptation. The experiment results show that the proposed DCS-based method not only estimates the multipath channel components accurately but also achieves higher CE performance than classical Orthogonal Matching Pursuit (OMP) method and other traditional DCS methods in the time-frequency dual selective channels.

A joint DOA and polarization estimation method based on the conformal polarization sensitive array from the sparse reconstruction perspective

The conformal polarization sensitive array (CPSA) is formed by placing some vector sensors on the conformal array and it has a wide range of practical application in direction of arrival (DOA) and polarization parameters estimation. However, due to the diversity of each sensor’s direction, the performance of the conventional parameters estimation methods based on the CPSA would decrease greatly, especially under the low signal to noise ratio (SNR) and limited snapshots. In order to solve this problem, a unified framework and sparse reconstruction perspective for joint DOA and polarization estimation based on CPSA is proposed in this paper. Specifically, the array received signal model of the CPSA is formulated first and the two-dimensional spatial sparsity of the incident signals is then exploited. Subsequently, after employing the singular value decomposition method to reduce the dimension of array output matrix, the variational sparse Bayesian learning and orthogonal matching pursuit methods are utilized to solve the source DOA estimation, respectively. Finally, the polarization parameters are obtained by the minimum eigenvector method. Simulation results demonstrate that the novel approaches can provide improved estimation accuracy and resolution with low SNR and limited snapshots.

Dynamic ISAR Imaging Method for Multiple Moving Vehicles Based on OMP-CADMM

Inverse synthetic aperture radar (ISAR) technology has attracted considerable attention in smart traffic monitoring, owing to the superiority of high-resolution imaging and tracking for moving targets in all-weather. However, in practical application cases, it is hard to obtain a globally-focused image of multiple vehicles by traditional ISAR imaging techniques due to the nonuniform motions of vehicles. Hence, a dynamic ISAR imaging method for multiple moving vehicles based on the joint of orthogonal matching pursuit (OMP) and consensus alternating direction method of multipliers (CADMM) is proposed in this paper. First, the preprocessing for raw data is performed in the wavenumber domain to simplify the imaging task into linear phase error estimation and distributed image recovery. Based on the sparsity of moving vehicles, the OMP method is utilized to estimate the dynamic motion phase error of consecutive frames data for different moving vehicles with less computational overhead. Then, the dynamic ISAR imaging problems of multiple moving vehicles can be transformed into the distributed imaging problem with variously estimated phases. Motivated by this fact, the CADMM optimization framework is exploited for the distributed ISAR imaging problem to obtain a globally-focused result according to the consensus constraint characteristic of multiple vehicles. Lastly, both the simulation and real data experiments are conducted to verify the performance and feasibility of the OMP-CADMM method. Furthermore, the experimental results show that the proposed method is capable of dynamic imaging and de-noising for multiple vehicles without signal separation.

Downlink Wideband Channel Estimation for Asymmetrical Full-Digital System

This letter considers downlink wideband channel estimation in an asymmetrical full-digital system where the number of uplink receive radio frequency chains is less than that of the downlink. This channel inconsistency will reduce downlink channel estimation accuracy. To deal with this problem, we adopt the coprime array topology in uplink receive antennas. Then, two iterative algorithms which are based on alternating direction method of multipliers and block-sparsity orthogonal matching pursuit, respectively, are developed to rebuild downlink channel. Simulation results demonstrate the effectiveness of the proposed scheme in the asymmetrical full-digital system.

Deep Learning Compressed Sensing-Based Beamspace Channel Estimation in mmWave Massive MIMO Systems

Channel estimation attaches great importance in millimeter wave (mmWave) massive multiple input multiple output (MIMO) systems. This letter proposes a two-step orthogonal matching pursuit (OMP) method to estimation channel state information (CSI) based on deep learning compressed sensing. Specifically, in the first-step OMP, a composite convolution kernel function (CKF) is designed for coarsely estimating angles of arrival/departure (AoAs/AoDs) from correlation matrix. In the second-step OMP, a Squeeze-and-Excitation Residual network (SE-Resnet) with Noise2Void (N2V) learning strategy is presented to denoise correlation matrix and finely estimate AoAs/AoDs. The proposed method can work without labeled data. Simulation shows that the two-step OMP significantly outperforms state-of-the-art mmWave channel estimation methods. Moreover, it works robustly in low signal-to-noise ratio (SNR) regimes with a small number of training frames.

An Orthogonal Matching Pursuit Variable Screening Algorithm for High-Dimensional Linear Regression Models

Variable selection plays an important role in data mining. It is crucial to filter useful variables and extract useful information in a high-dimensional setup when the number of predictor variables d tends to be much larger than the sample size n . Statistical inferences can be more precise after irrelevant variables are moved out by the screening method. This article proposes an orthogonal matching pursuit algorithm for variable screening under the high-dimensional setup. The proposed orthogonal matching pursuit method demonstrates good performance in variable screening. In particular, if the dimension of the true model is finite, OMP might discover all relevant predictors within a finite number of steps. Throughout theoretical analysis and simulations, it is confirmed that the orthogonal matching pursuit algorithm can identify relevant predictors to ensure screening consistency in variable selection. Given the sure screening property, the BIC criterion can be used to practically select the best candidate from the models generated by the OMP algorithm. Compared with the traditional orthogonal matching pursuit method, the resulting model can improve prediction accuracy and reduce computational cost by screening out the relevant variables.

Time-Delay Estimation by Enhanced Orthogonal Matching Pursuit Method for Thin Asphalt Pavement With Similar Permittivity

Time-delay estimation (TDE) for thin top layers of asphalt pavement is a challenging task due to the limited resolution of ground penetrating radar (GPR) as well as small permittivity difference between top layers. Echoes backscattered from the interfaces of top layers with similar permittivity have usually much smaller amplitudes compared with other echoes, which can be called weak signals. The weak backscattered echoes are usually too sensitive to the noise and other strong echoes that current signal processing approaches (subspace-based methods and compressed sensing based methods) might have false estimation results even failures without proper processing of them. Therefore, in this paper, an enhanced orthogonal matching pursuit (OMP) method is proposed to deal with weak signals resulting from similar permittivity of adjacent asphalt layers. Based on the orthogonality between signal and noise subspaces, we firstly apply the truncated singular value decomposition (SVD) on the received signals, in order to reduce the noise impact. Secondly, we build an orthogonal matrix to the mode matrix of the pre-estimated strong backscattered echoes, and map it to the overcomplete dictionary matrix, such that the influence of the residual of the strong backscattered echoes can be reduced. Finally, the time-delays of backscattered echoes and layer thicknesses are estimated. Compared with conventional approaches, the proposed method is more suitable for TDE in thin asphalt pavement detection. The accuracy of the proposed method is validated by both numerical and experimental data.

The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct Sparse Polynomials

The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct Sparse Polynomials

An OMP-TV2 algorithm for detecting white matter fiber crossings in brain MRI

This paper introduces a novel algorithm for solving non-Gaussian mixture models of diffusion tensor imaging (DTI). In particular, these models are used for detecting the orientations of white matter fibers in brain. In our approach, any DT-MRI model (mathematically) is represented by an under-determined system of linear equations. The proposed algorithm uses an orthogonal matching pursuit (OMP) method coupled with Tikhonov regularization for solving such an under-determined system effectively, which results in better reconstruction of the fibers orientation. These linear systems depend on the number of the gradient directions used for generating the signals and for reconstruction process. OMP is a greedy iterative algorithm that picks the column of coefficient matrix that has the maximum correlation or projection on the residual at each stage. Using OMP with Tikhonov regularization shows tremendous reduction in the angular error when compared with an existing scheme where non-negative least square method (NNLS) is used. The proposed work is validated with both artificial simulations as well as real data experiments. The reduction in angular error is more pronounced when the angle of separation between the fibers is small.

Adaptive Channel Estimation for Underwater Acoustic OFDM System in Impulsive Noise Environment

Applying the orthogonal matching pursuit (OMP) to estimate the underwater acoustic (UWA) orthogonal frequency division multiplexing (OFDM) channels is attractive because of its high estimation accuracy and low computational cost. However, most existing OMP-based algorithms suffer the limited estimation accuracy in impulsive noise (IN) cases. Through the studies can be found, only part of channels’ estimation is affected due to the random IN which appears transient and intermittent in time and frequency. Based on this observation, joint time-frequency OMP (JTF-OMP) method is proposed, where the estimation of the affected channels benefits adaptively from that of adjacent channels in time or frequency. It is well known that preliminary Doppler scale estimation is key to the subsequent OMP algorithm, which is difficult to deal with due to the IN. To solve this problem, an adaptive Doppler scale estimation (ADSE) method is proposed. It involves generating two shorter identical cyclic prefixes (CPs) for each OFDM symbol, placed before two adjacent OFDM symbols. The repetition pattern can adaptively defend the IN which appears randomly and shortly in time. Simulation results show that the proposed algorithms integrating JTF-OMP with ADSE can achieve much higher estimation accuracy and better system reliability than the OMP in the IN environment.

Double-Norm Constrained Image Denoising Algorithm Based on Dictionary Learning Sparsity and FCM Structure Clustering

To solve the problem of image smoothness and fuzzy edge texture information after image denoising, proposed a new image denoising method based on dictionary learning. Firstly, the external cycling principal component analysis reduces the dimensions of image data while retaining the main data and constructing the learning dictionary. Secondly, used the fuzzy c-means structure clustering method internally to implement structural constraints on learning dictionary training, which considered the internal structure of image pixels. Then, the learning dictionary under the double constraints of sparse and structural clustering is obtained by internal and external iteration. Finally, the sparse representation coefficient and redundancy dictionary are obtained by the orthogonal matching pursuit method and alternate direction multiplier method, and the denoised images are estimated and updated according to sparse coding theory. Using the grayscale image from Set12 data set, color image from the CBSD68 data set, real noise from RENOIR data set, and texture image from USC-SIPI data set. The experimental results show that compared with the model-based algorithms (KSVD, ISKR, EPLL, NCSR, and LR-GSC) and the learning-based algorithms(DnCNN, IRCNN, and FFDNet), the proposed algorithm preserves the edge and texture information of the image better, and achieves better subjective visual effects and objective numerical results, especially for the image with complex structure and content, and the running time is much less than learning-based algorithms.