Matching Pursuit Algorithm Research Articles

A Fast and Super-Resolution Method of Vortex-Based Imaging

With characteristics of particular wavefronts and orthogonal modes, the sparse imaging method based on vortex waves could obtain high-resolution reconstruction. However, building a large-scale observation matrix is time-consuming and heavily burdens the whole imaging procedure. Inspired by the spherical harmonic expansion of plane waves, this paper provides a fast super-resolution imaging method based on vortex waves. Featuring spherical harmonic functions and a transformation, an orthogonal matching pursuit algorithm for high-resolution imaging exploits a low-rank matrix decomposition of the observation matrix. Simulation results show that the proposed method exhibits significant efficiency advantages while retaining high resolution, achieving an efficiency of up to 51.4% when applied to a large-scale observation matrix.

Sparse decomposition enables adaptive and accurate Raman spectral denoising

Enhancing the quality of spectral denoising plays a vital role in Raman spectroscopy. Nevertheless, the intricate nature of the noise, coupled with the existence of impurity peaks, poses significant challenges to achieving high accuracy while accommodating various Raman spectral types. In this study, an innovative adaptive sparse decomposition denoising (ASDD) method is proposed for denoising Raman spectra. This approach features several innovations. Firstly, a dictionary comprising spectral feature peaks is established from the input spectra by applying a chemometric feature extraction method, which better aligns with the original data compared to traditional dictionaries. Secondly, a dynamic Raman spectral dictionary construction technique is introduced to swiftly adapt to new substances, employing a limited amount of additional Raman spectral data. Thirdly, the orthogonal matching pursuit algorithm is utilized to sparsely decompose the Raman spectra onto the constructed dictionaries, effectively eliminating various random and background noises in the Raman spectra. Empirical results confirm that ASDD enhances the accuracy and robustness of denoising Raman spectra. Significantly, ASDD surpasses existing algorithms in processing Raman spectra of pesticide.

Integrated thrust ripple identification and compensation for linear servo system using an MP algorithm

Generally there are two methods for the thrust ripple modeling: one is to identify the eigenvalues and the model parameters of thrust ripple sequentially under rigorous operating conditions; another is to treat thrust ripple as a general and inaccurate disturbance. To get rid of the constraints and further enhance the tracking accuracy of the linear servo system, a novel integrated identification and compensation scheme using an improved matching pursuit algorithm is proposed in this paper. First, the dynamics of the linear motor is formulated, and the cause of thrust ripple is analyzed. Then, a time–frequency atomic library of thrust ripple is constructed with the consideration of the frequency characteristics of position command, and meanwhile, the two optimal atoms are obtained successively by maximizing the inner product for the thrust ripple reconstruction. Based on the above, the eigenvalues and model parameters of thrust ripple can be simultaneously identified in an online manner. Finally, the feedforward compensation component is devised by the identification results to suppress thrust ripple. In order to verify the superiority of the proposed scheme, simulations and experiments are conducted compared with the conventional methods.

Orthogonal matching pursuit algorithm based on weighted cosine similarity for sound source localization

Abstract Compressive sensing overcomes the limitations of the Nyquist criteria and is one of the most widely used compressive sensing reconstruction algorithms. Orthogonal matching pursuit (OMP) algorithm is simple, in terms of hardware implementation, and has high computational efficiency. However, the OMP algorithm exhibits poor identification performance for low-frequency sound sources and results in large localization deviations when the mesh spacing of the focus plane is small. In this study, a novel atom selection criterion based on weighted cosine similarity was proposed to improve the OMP algorithm for sound source localization and characterization. This method replaces the original inner product criterion to measure the correlation between the column vectors of the sensing matrix and the residuals, which addresses the atom selection error caused by the high correlation between atoms. Numerical simulations and experimental results show that the proposed method has a stronger anti-noise interference capability and higher accuracy for sound source identification with fewer sampling points, particularly in low-frequency and low signal-to-noise ratio environments. Compared to other OMP algorithms, the proposed method improves the performance of the OMP algorithm in sound source localization and widens the sound frequency range. This study is valuable for achieving highly accurate sound source localization and reducing measurement costs in practical applications.

Efficient Compressed Sensing Reconstruction Algorithm for Nonnegative Vectors in Wireless Data Transmission

With the rapid development of 5G communication and wireless Internet of Things technology, the application of intelligent wearable devices based on wireless data transmission technology is becoming more and more popular. However, due to the bandwidth of wireless data transmission nodes and the power consumption of the device system, the use time and data storage of wearable devices are severely restricted. The compressed sensing (CS) technology has become an effective method to tackle this problem. CS technology includes data compressive sensing at the transmission end and data reconstruction at the receiving end. In this paper, we consider the reconstruction of nonnegative sparse vectors, an important problem in the area of CS for wireless data transmission. It is known that the interval-passing (IP) algorithm is a low-complexity message-passing type method for the problem. However, the reconstruction performance of the IP algorithm is inferior to that of the other state-of-the-art CS reconstruction algorithms such as the orthogonal matching pursuit (OMP) algorithm. In order to address the problem, we propose a two-stage reconstruction algorithm in this paper. The proposed algorithm applies the IP algorithm for the first stage of reconstruction. If the reconstruction fails, the OMP algorithm is then used on the basis of the results in the first stage. The proposed algorithm is evaluated and compared with other state-of-the-art algorithms by the probability of perfect reconstruction under the given sparsity order value. Simulation results suggest that the proposed two-stage algorithm can greatly improve the reconstruction performance of the IP algorithm and can even outperform the OMP algorithm. In addition, the low-complexity advantages of the IP algorithm are maintained in the proposed algorithm.

A wavefield reconstruction method using sparse representation and dictionary learning for RTM

Abstract Reverse time migration (RTM) is a well-established imaging technique that uses the two-way wave equation to achieve high-resolution imaging of complex subsurface media. However, when using RTM for reverse time extrapolation, a source wavefield needs to be stored for cross-correlation with the backward wavefield. This requirement results in a significant storage burden on computer memory. This paper introduces a wavefield reconstruction method that combines sparse representation to compress a substantial amount of crucial information in the source wavefield. The method uses the K-SVD algorithm to train an adaptive dictionary, learned from a training dataset consisting of wavefield image patches. For each timestep, the source wavefield is divided into image patches, which are then transformed into a series of sparse coefficients using the trained dictionary via the batch-orthogonal matching pursuit algorithm, known for its accelerated sparse coding process. This novel method essentially attempts to transform the wavefield domain into the sparse domain to reduce the storage burden. We used several evaluation metrics to explore the impact of parameters on performance. We conducted numerical experiments using acoustic RTM and compared two RTM methods using checkpointing techniques with two strategies from our proposed method. Additionally, we extended the application of our method to elastic RTM. The conducted tests demonstrate that the method proposed in this paper can efficiently compress wavefield data, while considering both computational efficiency and reconstruction accuracy.

An iterative thresholding-based algorithm for brain–computer interface (BCI) application

The EEG signals are recorded using surgical (invasive) or non-surgical (non-invasive) BCI neuroimaging modalities. Basically, we are dealing with a huge amount of data and long signal recordings.The classic solution to deal with the huge amount of data has been data compression, where the data is first collected in its original large format and then converted to a compressed format of smaller size for storage or transmission. This has become a traditional solution to the problem of handling the massive volume of data.Compressive sensing is a novel technique that senses the signal in a compressed format using a sub-Nyquist–Shannon sampling rate and reconstructs it when the data from the compressed sensed signal is required.In the context of applying CS, the first issue is how to construct the linear measurement matrix to ensure that compressive sensing meets the requirements of the application. The second issue depends on the way in which the sparse signal can be obtained from a small sample of observations. In this paper, nuclear norm minimization is proposed to enforce sparsity and low-rank structures in the reconstructed multi-channel EEG signals. To compute the optimization, we propose two new algorithms which we call: a weighted thresholding algorithm and a weighted thresholding orthogonal matching pursuit algorithm based on compressive sensing. We perform the experiments on the insomnia EEG dataset. Computer simulations provide and show the good behavior of these algorithms and the NNM norm, compared to others in the literature.

Recovery performance improvement of image compressive sensing using complex‐valued Vandermonde matrix

AbstractHere, a novel image‐based quantized compressive sensing (QCS) framework based on complex‐valued Vandermonde (Vander) matrix is proposed. In the proposed QCS framework, a discrete wavelet transform (DWT) serves as a sparse basis and a partial complex‐valued Vander matrix serves as a measurement matrix. The theoretical analysis based on mutual coherence metric of compressive sensing (CS) theory shows that the proposed Vander measurement matrix has the best reconstruction performance among other conventional measurement matrices. The simulation results also show that the recovery quality using the proposed measurement matrix can be greatly improved compared with the other existing real‐valued measurement matrices. In particular, the experiment results also show that under the same measurement matrix, the reconstruction performance of Smoothed l0 norm (SL0) algorithm is better than that of Orthogonal Matching Pursuit (OMP) algorithm, sparsity adaptive matching pursuit (SAMP) algorithm and approximate message passing (AMP) algorithm. In addition, a sparse measurement matrix scheme is further proposed to achieve a trade‐off between recovery performance and computational complexity. The theoretical analysis and simulation results both show the proposed image‐based QCS is efficient.

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.

Multiple Line Outage Detection for Power Systems Based on Binary Matching Pursuit

Line outage detection plays a key role in black-out prevention and recovery in power systems. Considering the number of outage lines is sparse as compared to total transmission lines in the early line outage stage, compressive sensing theory is applied to study the multiple line outage detection of power systems. By formulating the sparse line outage detection problem in a standard compressive sensing form, a binary matching pursuit algorithm is proposed to solve the problem. A dice coefficient and an atom exclusion strategy are subsequently introduced to improve the detection accuracy of the proposed algorithm. Algorithm complexity has also been analyzed. Simulation results demonstrate that the proposed algorithm not only has more resilience to noise and less sensitivity to the data sampling size, but also shows lower computational burden and higher detection efficiency.

Model-Driven Deep-Learning-Based Underwater Acoustic OTFS Channel Estimation

Accurate channel estimation is the fundamental requirement for recovering underwater acoustic orthogonal time–frequency space (OTFS) modulation signals. As the Doppler effect in the underwater acoustic channel is much more severe than that in the radio channel, the channel information usually cannot strictly meet the compressed sensing sparsity assumption in the orthogonal matching pursuit channel estimation algorithm. This deviation ultimately leads to a degradation in system performance. This paper proposes a novel approach for OTFS channel estimation in underwater acoustic communications, utilizing a model-driven deep learning technique. Our method incorporates a residual neural network into the OTFS channel estimation process. Specifically, the orthogonal matching pursuit algorithm and denoising convolutional neural network (DnCNN) collaborate to perform channel estimation. The cascaded DnCNN denoises the preliminary channel estimation results generated by the orthogonal matching pursuit algorithm for more accurate OTFS channel estimation results. The use of a lightweight DnCNN network with a single residual block reduces computational complexity while still preserving the accuracy of the neural network. Through extensive evaluations conducted on simulated and experimental underwater acoustic channels, the outcomes demonstrate that our proposed method outperforms traditional threshold-based and orthogonal matching pursuit channel estimation techniques, achieves superior accuracy in channel estimation, and significantly reduces the system’s bit error rate.

Assessment of The Impact of Blasting Works on Buildings Located in the Vicinity of Open-Pit Mines Using Matching Pursuit Algorithm

Assessment of The Impact of Blasting Works on Buildings Located in the Vicinity of Open-Pit Mines Using Matching Pursuit Algorithm

SCWOMP Recovery Algorithm for 5G MIMO Communication Symbol Detection

In order to solve the problem of small capacity and high energy consumption in China’s 5G communication technology system, the research proposes that based on the segmented weakly orthogonal matching pursuit (SWOMP) algorithm, it is combined with the compressed sensing matching pursuit algorithm to form a segmented backtracking weak selection positive algorithm and Cross Match Tracking (SCWOMP) algorithm. First, the sparseness of MIMO system technology and its transmission structure is analyzed. Then, the new model is built after comparing with other algorithms, and the problem of overestimating the low recovery probability in the calculation process is improved by the backtracking of the algorithm and the improvement of the angle of the atomic column selection, so as to reduce the number of iterations and improve the performance of the algorithm. The results show that, in the performance comparison of different sampling points under different compressed sensing recovery algorithms, the recovery probability of the SCWOMP algorithm is the best, and when the number of sampling points is 80, although the fixed step size of the SCWOMP algorithm is different, there is recovery. The probability has a maximum value, close to 1. Then, the improved compressed sensing recovery algorithm is simulated and analyzed. When the pruning coefficient is 0.5 and the number of sampling points is 80, the reconstruction rate has a maximum value, and when other algorithms reach the maximum reconstruction rate, the number of sampling points (M) is significantly greater than that of the SCWOMP algorithm. An increase in the rate of reduction of the reconstruction probability of the SCWOMP algorithm is significantly lower than that of other algorithms; when sparsity is equal to 70, the reconstruction probability becomes 0, indicating that SCWOMP has a wider reconfigurable range and has a significant performance effect. This shows that the proposed SCWOMP algorithm has the best detection performance for 5G communication symbol detection, which can effectively increase the capacity of the system and better promote technology.

Matching Pursuit for Denoising Raman Spectra, Based on Genetic Algorithm and Hermite Atoms.

Due to its various advantages, Raman spectroscopy has become a powerful tool in different fields of science and engineering; however, in specific applications, this technique's limiting factor is closely related to the inherent noise of the Raman spectra. To eliminate the noise of a Raman spectrum, preserving its position, intensity, and width characteristic, we propose using a genetic matching pursuit-Hermite atoms (GMP-HAs) algorithm in this work. This algorithm helps recover Raman spectra immersed in Gaussian noise with the least number of atoms. The noise-free Raman signal is reconstructed with the GMP-HAs algorithm, transforming the typical best-matching atom search into an optimization problem. Specifically, we maximize the fitness function, defined as the correlation between current residual and Hermite atoms, with the genetic algorithm MI-LXPM encoded in a real domain and avoiding local maxima, by adding a stopping criterion based on an exponential adjustment according to the algorithm's behavior in the presence of noise. Simulated and biological Raman spectra are used to evaluate the proposed algorithm and compare its performance with typically known methods for denoising, such as the Savitzky- Golay filter (SG) and basis pursuit denoising. Using the signal-to-noise ratio (S/N)metric resulted in a 0.31 dB advantage in the S/N product for the proposed algorithm with respect to SG. Additionally, it is shown that the algorithm uses only 25.3% of the number of atoms needed by the matching pursuit algorithm. The results indicate that the GMP-HAs algorithm has better denoising capabilities, and at the same time, the Raman spectra are decomposed with fewer atoms compared to known sparse algorithms.

Underwater Acoustic Channel Estimation via an Orthogonal Matching Pursuit Algorithm Based on the Modified Phase-Transform-Weighted Function

In the context of torpedo guidance systems, the performance of active sonar in channel parameter estimation and target detection and recognition is significantly degraded by the multipath effect and the time-varying characteristics of the underwater acoustic (UWA) channel. Therefore, it is urgent to propose an algorithm that can accurately estimate the channel parameters in multipath time-varying UWA channels. To solve these problems, this study developed a modified phase transform (PHAT)-weighted function and applied it to the orthogonal matching pursuit (OMP) algorithm, named M-PHAT-OMP. The proposed algorithm is more robust, improves the resolution of the time delay and further improves the estimation accuracy of the parameters in the case of motion. Furthermore, with the aim of solving the problem of the difficulty that the traditional OMP algorithm has in determining sparsity, this study proposes a joint-threshold method, where the threshold value serves as the condition for terminating the algorithm’s iteration. The simulation results demonstrate that the M-PHAT-OMP algorithm proposed in this study exhibits a superior performance compared to other algorithms, as evidenced by its lower root mean square error (RMSE) for delay. Moreover, the experimental results also validate that the proposed algorithm has superior robustness and resolution of the time delay in practical applications.

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.

Logistic Regression Matching Pursuit algorithm for text classification

Text classification is a challenging problem due to the high dimensionality of the text, which can limit classification performance. The orthogonal matching pursuit (OMP) algorithm is one of the most popular sparse recovery algorithms. An OMP based text classification algorithm, called the Logistic-OMP algorithm, was recently proposed by Skianis et al.. Simulation tests indicate that Logistic-OMP has excellent performance in text dimensionality reduction. This paper optimizes the Logistic-OMP algorithm, and proposes a new text classification algorithm called the Logistic Regression Matching Pursuit (LRMP) algorithm. The LRMP algorithm defines a new loss function and residual update function. It requires only one iteration to solve the negative log likelihood minimization problem, and its classification performance is guaranteed by the strong Wolfe condition, which makes it optimizes the classification accuracy while significantly speeding up the training speed. Simulation tests on topic classification and sentiment analysis from 20Newsgroups, Amazon product reviews, and movie reviews datasets show that the LRMP algorithm has a shorter computation time of a single iteration than the Logistic-OMP algorithm, with a total training time of 8.08%–21.16% shorter than that of the Logistic-OMP algorithm, and the memory usage is 3.20%–6.21% lower than that of the Logistic-OMP algorithm. Furthermore, the average Accuracy and F1-Score of the LRMP algorithm are improved by 1.61%–26.55% and 1.83%–25.46%, respectively, compared with the benchmark classifier. Compared with the advanced classifiers (including Logistic-OMP), the average Accuracy and F1-Score of the LRMP algorithm are improved by 0.46%–8.97% and 0.57%–9.40%, respectively.

On the Application of the Stability Methods to Time Series Data

The important problem of selecting the predictors in a high-dimensional case where the number of candidates is larger than the sample size is often solved by the researchers from the signal processing community using the orthogonal matching pursuit algorithm or other greedy algorithms. In this work, we show how the same problem can be solved by applying methods based on the concept of stability. Even if it is not a new concept, the stability is less known in the signal processing community. We illustrate the use of stability by presenting a relatively new algorithm from this family. As part of this presentation, we conduct a simulation study to investigate the effect of various parameters on the performance of the algorithm. Additionally, we compare the stability-based method with more than eighty variants of five different greedy algorithms in an experiment with air pollution data. The comparison demonstrates that the use of stability leads to promising results in the high-dimensional case.

Data evaluation algorithm for compensation litigation for ecotope pollution damage in the Yellow River valley caused by industrial wastewater from the perspective of green development.

Since the reform and opening up, China's economy has achieved amazing growth. At the same time of industrialization transformation, the traditional high-energy consumption and external growth model has brought serious environmental problems, and the pollution control situation is facing many difficulties. The Yellow River Valley gives birth to the Chinese civilization. With the formulation of the national strategy for ecological protection and high-quality development in the Yellow River Basin and the demand for green development, the control of industrial pollution has become the main task of environmental protection in the Yellow River Basin. However, the research on the ecotope pollution in the Yellow River Valley mainly stays in the theory and strategy. In response to the above problems, this paper would carry out scientific data analysis and high-dimensional research on the ecotope pollution in the Yellow River Valley from the perspective of green development and data analysis algorithms. The research results showed that the reconstruction probability of the Threshold-based Sparsity Adaptive Matching Pursuit (TSAMP) algorithm remained 100% when K was less than 50.

Sensing User's Channel and Location With Terahertz Extra-Large Reconfigurable Intelligent Surface Under Hybrid-Field Beam Squint Effect

This paper investigates the sensing of user's uplink channel and location in terahertz extra-large reconfigurable intelligent surface (XL-RIS) systems, where the unique hybrid far-near field effect and the beam squint effect caused by the XL array aperture as well as the XL bandwidth are overcome. Specifically, we first propose a joint channel and location sensing scheme, which consists of a location-assisted generalized multiple measurement vector orthogonal matching pursuit (LA-GMMV-OMP) algorithm for channel estimation (CE) and a complete dictionary based localization (CDL) scheme, where a frequency selective polar-domain redundant dictionary is proposed to overcome the hybrid field beam squint effect. The CE module outputs coarse on-grid angle estimation (respectively observed from the BS and RIS) to the localization module, which returns the fine off-grid angle estimation to improve CE. Particularly, with RIS, CDL can obtain user's location via line intersection, and a polar-domain gradient descent (PGD) algorithm at the base station is proposed to achieve the off-grid angle estimation with super-resolution accuracy. Additionally, to further reduce the sensing overhead, we propose a partial dictionary-based localization scheme, which is decoupled from CE, where RIS is served as an anchor to lock the user on the hyperbola according to time difference of arrival and the user's off-grid location can be obtained by using the proposed PGD algorithm. Simulation results demonstrate the superiority of the two proposed localization schemes and the proposed CE scheme over state-of-the-art baseline approaches.