Sparsity Adaptive Matching Pursuit Research Articles

Single-photon lidar depth imaging based on sparsity adaptive matching pursuit method

Photon counting lidar has the ability to detect weak echo photons. However, in imaging applications, a small number of echo signals obtained in a very short acquisition time cannot get an accurate image estimation through the photon arrival time distribution histogram. Therefore, high-precision and fast imaging of an object using a small amount of weak echo photon signals is urgent to be solved. In this work, a sparse adaptive matching pursuit (SAMP) algorithm is proposed to process the echo photons without prior information to obtain the effective photon interval, which improves the reconstruction quality and imaging speed. By constructing a non-coaxial scanning imaging system to detect the face model, it has been experimentally proven that the proposed algorithm can achieve depth and reflectance image estimation under the condition of low power and low acquisition time of 4µs per pixel on average, and the mean absolute error (MAE) value is reduced by about 10 times compared to conventional reconstruction algorithm.

Detection and recovery of anomalous vibration signal of rotating machinery based on LOF-MSAMP

The collected vibration signals of rotating machinery contain pulses, missing, and other low-quality anomalous data due to environmental noise interference, unstable data transmission, and data acquisition instrument failure. These low-quality data obstruct the analysis of the healthy operation condition of rotating machinery. This paper proposes a method for anomalous vibration signal detection and recovery based on the local outlier factor algorithm and the modified sparsity adaptive matching pursuit algorithm. The method combines the local outlier factor algorithm and compressive sensing theory to realize anomalous vibration signal detection and recovery. This paper evaluates the recovery performance both qualitatively and quantitatively and discusses how the proposed method’s hyperparameter selection affects the recovery results. A set of simulated signal and measured hob base signal are used to verify the proposed method. The results indicate that, when compared to the other seven reconstruction algorithms, the proposed method’s recovered signal has the lower error level and the higher waveform similarity which reaches more than 98% to the original signal, effectively improving data quality.

Target Detection Method Based on Adaptive Step-Size SAMP Combining Off-Grid Correction for Coherent Frequency-Agile Radar

Coherent frequency-agile radar (FAR) has a low probability of intercept (LPI) and excellent performance of electronic counter-countermeasures (ECCM) and electromagnetic compatibility, which can improve radar cooperation and survivability in complex electromagnetic environments. However, due to the nonlinearity of radar carrier frequency and the limitation of the Doppler tolerance of high-resolution range cells, the undesirable blind-speed sidelobes are generated in the two-dimensional (2D) range–velocity plane after coherent integration (CI) using the traditional methods based on a matching filter, which may degrade the target detection performance. To solve this problem, an adaptive step-size sparsity adaptive matching pursuit (SAMP) algorithm combining off-grid correction (ASSAMP-OC) is proposed in this paper, which seeks to achieve a better trade-off between recovery efficiency and detection performance. Firstly, an adaptive iteration step size based on the Spearman correlation coefficients (SCCS) is devised, which solves the problem of the traditional SAMP algorithm being insensitive to the change in iteration step size when the residuals vary slightly, and improves the recovery speed. Secondly, the off-grid correction method by combining a regularized stagewise backtracking idea and gradient descent optimization (GDO) is adopted to improve the recovery accuracy and suppress the blind-speed sidelobe energy (BSSE), which helps to reduce CI gain loss and improve the target detection performance without the prior information of the sparsity lever. Finally, simulation and experimental results demonstrate the effectiveness and efficiency of the proposed method in terms of target detection probability, target signal energy ratio after recovery, and computational cost, compared to several existing methods.

Fast Dynamic Phasor Estimation Algorithm Considering DC Offset for PMU Applications

Because of the volatility and intermittence of the renewable energy units in the novel power system, the electrical variables usually exhibit dynamic characteristics. Under fault conditions, the electrical variables usually contain a decaying DC (DDC) component. Currently, when considering the DDC component and the dynamic characteristics of electrical variables, it is difficult to obtain highly precise estimation results in most references. In this paper, a fast dynamic phasor estimation algorithm considering the DC offset is proposed to obviate errors caused by dynamic characteristics and the DDC component. The algorithm consists of two parts. The first part establishes the mathematical model of DDC using exponential functions and obtains the exact DDC component by iteration. The second part establishes the compressive sensing Taylor Fourier Multi-Frequency (CSTFM) model of the dynamic phasor. The improved sparsity adaptive matching pursuit (ISAMP) algorithm is used to quickly and accurately estimate the dynamic phasor, frequency and rate of change of frequency (ROCOF). Simulation and field data test results show that the proposed algorithm can accurately estimate the fault current phasor, frequency, and ROCOF compared with existing phasor estimation algorithms.

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.

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.

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.

Improved sparsity adaptive matching pursuit algorithm based on compressed sensing

Traditional greedy algorithms need to know the sparsity of the signal in advance, while the sparsity adaptive matching pursuit algorithm avoids this problem at the expense of computational time. To overcome these problems, this paper proposes a variable step size sparsity adaptive matching pursuit (SAMPVSS). In terms of how to select atoms, this algorithm constructs a set of candidate atoms by calculating the correlation between the measurement matrix and the residual and selects the atom most related to the residual. In determining the number of atoms to be selected each time, the algorithm introduces an exponential function. At the beginning of the iteration, a larger step is used to estimate the sparsity of the signal. In the latter part of the iteration, the step size is set to one to improve the accuracy of reconstruction. The simulation results show that the proposed algorithm has good reconstruction effects on both one-dimensional and two-dimensional signals.

A Correlation Coefficient Sparsity Adaptive Matching Pursuit Algorithm

This paper presents a correlation coefficient sparsity adaptive matching pursuit (CCSAMP) algorithm for practical compressed sensing (CS). The sparsity adaptive matching pursuit (SAMP) has been enhanced using the CCSAMP algorithm. The CCSAMP's capacity to accurately reconstruct the signal with fewer repetitions is its most novel characteristic when compared to other state-of-the-art SAMP enhancement methods. This makes it a candidate for many practical applications that need fast reconstruction. The proposed algorithm constructs two correlation vectors, which represent the input signals recovered from the support set and candidate set. The step size is transformed by their Pearson correlation coefficients (PCCS). Compared to the residual energy, the correlation coefficient is more sensitive. The CCSAMP reduces the number of iterations while maintaining the SAMP's capability of signal reconstruction without prior knowledge of the sparsity. Simulation shows that the CCSAMP can significantly reduce the number of iterations compared to the SAMP algorithm. The CCSAMP can be used for radar detection, radar 3D imaging, and other fields where fast and accurate reconstruction of signals is required.

An Improved Structural Health Monitoring Method Utilizing Sparse Representation for Acoustic Emission Signals in Rails

The structural health of rails significantly impacts the safety of railway transport, which requires long-term and accurate monitoring. An improved structural health monitoring (SHM) method is proposed to enhance the damage information and construct an adaptive weighted index for evaluating the structural health states of rails. In this method, modified singular value decomposition (SVD) with a double-layer Hankel matrix compensation algorithm enhances the damage information and ensures real-time detection. Based on the inflection point of the inner product gradient, the step size of the sparsity adaptive matching pursuit (SAMP) algorithm is adaptively adjusted to reconstruct damage signals. Subsequently, an innovative index is constructed with adaptive weighting for SHM of rails. Tensile tests are performed to verify the effectiveness of the proposed method. The results show that the proposed method avoids the defects of traditional nondestructive testing (NDT) techniques that rely on a priori information about the damage signal (such as damage frequency acoustic emission (AE) hits rate and waveform characteristics). Furthermore, using the variation in signal energy, the proposed method has the capability to accurately delineate the three structural health stages under complex waveform conditions, which is not possible with conventional detection methods. This method provides guidance for the damage analysis and monitoring techniques of rails.

Channel estimation for reconfigurable intelligent surface-assisted mmWave based on Re‘nyi entropy function

This study focuses on channel estimation for reconfigurable intelligent surface (RIS)-assisted mmWave systems, in which the RIS is used to facilitate base-to-user data transfer. For beamforming to work with active and passive elements, a large-size cascade channel matrix should always be known. Low training costs are achieved by using the mmWave channels’ inherent sparsity. The research provides a unique compressive sensing-based channel estimation approach for reducing pilot overhead issues to a minimum. The proposed technique estimates channel data signals in a downlink for RIS-assisted mmWave systems. The mmWave systems often have a sparse distribution of signal sources due to the spatial correlations of the domains. This distribution pattern makes it possible to use compressive sensing methods to resolve the channel estimation issue. In order to decrease the pilot overhead, which is necessary to predict the channel, the proposed method extends the Re‘nyi entropy function as the sparsity-promoting regularizer. In contrast to conventional compressive sensing techniques, which necessitate an initial knowledge of the signal’s sparsity level, the presented method employs sparsity adaptive matching pursuit (SAMP) techniques to gradually determine the signal’s sparsity level. Furthermore, it introduces a threshold parameter based on the signal’s energy level to eliminate the sparsity level requirement. Extensive simulations show that the presented channel estimation approach surpasses the traditional OMP-based channel estimation methods in terms of normalized mean square error performance. In addition, the computational cost of channel estimation is lowered. Based on the simulations, our approach can estimate the channel well while reducing training overhead by a large amount.

Research on Compressed Sensing Spectrometry Based on Electro-Optical Transmittance Coding

To develop fast and integrated spectrometry, we present a new method of compressed sensing spectrometry based on electro-optical transmittance coding. A LiNbO3 electro-optic modulator was applied to a directly compressed measurement code in the spectral dimension. Subsequently, a sequential forward floating selection algorithm was employed to select the coding measurement matrix, and sparsity adaptive matching pursuit was used as a solver algorithm. The principle was analyzed, and the measurement system was built for verification experiments. The experimental results reveal that the spectral reconstruction relative error is in the order of 10−2, and the full width at half maximum of the spectral measurement is as high as 1.2 nm. The spectral resolution can reach approximately 0.4 nm in the visible light band range (0.38–0.78 μm) with 1024 spectral channels. The compressed ratio of the compressed sensing spectrometry is up to 1:29. Furthermore, the spectral signal measurement time is only 0.25 ms. The study demonstrates a novel method, which exhibits high precision, speed, high compressed ratio and hyperspectral resolution.

An Effective Scheme of Building Electromagnetic Map for Spectrum Sensing

To address the severe spectrum scarcity problem and achieve efficient green communications, we propose a new and practical scheme to obtain electromagnetic data (ED) and a composite electromagnetic map reconstruction method (CEMRM). The scheme uses a small number of sensing nodes to obtain incomplete sampled ED, then uses CEMRM to reconstruct complete ED according to the incomplete ED and builds realistic electromagnetic maps (EMs) in various propagation scenarios. Specifically, we firstly adopt kriging (KG) method to obtain the geography-based ED (GED) according to geographical correlation of the locations of the sampled ED. Meanwhile, a novel algorithm, named filtered subdistrict sparsity adaptive matching pursuit (FSSAMP), is proposed to obtain the pure ED (PED) according to electromagnetic correlation of the sampled ED. Then, weight factors are mapped into the above two types of data and the fast gradient projection (FGP) method is employed to obtain the highly accurate combined ED (CED). Based on the CED, the accurate and practical EMs can be drawn. Simulation results demonstrate that the proposed scheme can provide more accurate ED and EMs than existing benchmark schemes in various propagation scenarios, and the built EMs can provide accurate information for the assessment of spectrum resources utilization to make spectrum resources efficiently used.

A Novel Sparsity Adaptive Algorithm for Underwater Acoustic Signal Reconstruction.

In view of the fact that most of the traditional algorithms for reconstructing underwater acoustic signals from low-dimensional compressed data are based on known sparsity, a sparsity adaptive and variable step-size matching pursuit (SAVSMP) algorithm is proposed. Firstly, the algorithm uses Restricted Isometry Property (RIP) criterion to estimate the initial value of sparsity, and then employs curve fitting method to adjust the initial value of sparsity to avoid underestimation or overestimation, before finally realizing the close approach of the sparsity level with the adaptive step size. The algorithm selects the atoms by matching test, and uses the Least Squares Method to filter out the unsuitable atoms, so as to realize the precise reconstruction of underwater acoustic signal received by the sonar system. The experimental comparison reveals that the proposed algorithm overcomes the drawbacks of existing algorithms, in terms of high computation time and low reconstruction quality.

A Compressed Sensing Reconstruction Algorithm Based on Hyperbolic Function

The accuracy of the compressed sensing theory reconstruction algorithm is important for signal recovery. Sparsity Adaptive Matching Pursuit (SAMP) has a fixed step size in each iterative process of reconstruction, which has a significant impact on accuracy in actual use, often leading to overestimation and underestimation. In order to solve this problem, combined with the advantages of regular backtracking and variable step size, the article introduces the idea of retrospective in the atom selection stage. Then, the atoms are inspected using backtracking and re-screened. The algorithm uses regularization at the beginning to select atoms with higher energy and reduce the number of atoms in the candidate set at the threshold stage. During reconstruction, because the energy difference of the reconstructed signal decreases rapidly at the initial stage, and then the energy difference decreases slowly. This algorithm takes advantage of the large change rate of the hyperbolic function at the beginning and the slower change rate at the later stage. At first, a large step size is used. When the energy difference reaches a certain threshold, a small step size is used instead. After the actual simulation, the improved algorithm improves the reconstruction accuracy and the effect is better.

Vibration measurement method based on single-frame coded illumination and compressive sensing

A visual vibration measurement method based on single-frame coded illumination and compressive sensing is proposed. The projector projects concentric rectangles with different sizes at different time points in a single camera exposure. According to the size of the rectangles, the image collected by the camera is separated into different sub frames. The centroids of the concentric rectangles are considered as the virtual feature points to record the vibration information of the object. The projector operates according to the random unequal interval trigger signal, and the projection is used as the sampling signal to encode the measured object. Discrete cosine transform is used as sparse basis, and sparsity adaptive matching pursuit and spectral projected gradient for L1 minimization (SPGL1) are used for signal reconstruction. Simulation analysis shows that the proposed method is feasible, and SPGL1 algorithm is more suitable for our signal reconstruction. The experiments indicate that the maximum absolute error of the proposed method for frequency measurement is 0.2985 Hz, and the maximum relative error is 1.6587 × 10 − 3. It is also applicable to multi-frequency measurement.

An improved algorithm of segmented orthogonal matching pursuit based on wireless sensor networks

Aiming at the problems of low data reconstruction accuracy in wireless sensor networks and users unable to receive accurate original signals, improvements are made on the basis of the stagewise orthogonal matching pursuit algorithm, combined with sparseness adaptation and the pre-selection strategy, which proposes a sparsity adaptive pre-selected stagewise orthogonal matching pursuit algorithm. In the framework of the stagewise orthogonal matching pursuit algorithm, the algorithm in this article uses a combination of a fixed-value strategy and a threshold strategy to screen the candidate atom sets in two rounds to improve the accuracy of atom selection, and then according to the sparsity adaptive principle, the sparse approximation and accurate signal reconstruction are realized by the variable step size method. The simulation results show that the algorithm proposed in this article is compared with the orthogonal matching pursuit algorithm, regularized orthogonal matching pursuit algorithm, and stagewise orthogonal matching pursuit algorithm. When the sparsity is 35 < K < 45, regardless of the size of the perception matrix and the length of the signal, M = 128, N = 256 or M = 128, N = 512 are improved, and the reconstruction time is when the sparsity is 10, the fastest time between 25 and 25, that is, less than 4.5 s. It can be seen that the sparsity adaptive pre-selected stagewise orthogonal matching pursuit algorithm has better adaptive characteristics to the sparsity of the signal, which is beneficial for users to receive more accurate original signals.

A method for magnetotelluric data processing based on sparsity adaptive stage-wise orthogonal matching pursuit

In order to effectively suppress large-scale strong interference and retain the useful low-frequency information of the measured magnetotelluric (MT) data, a new method of MT signal-noise separation based on sparsity adaptive stage-wise orthogonal matching pursuit (SAStOMP) is proposed. To demonstrate this technique, pulse atoms, cosine atoms and other atoms were used to build an over-complete dictionary, and fuzzy entropy was applied to control the sparsity of improved stage-wise orthogonal matching pursuit (IStOMP) algorithm, thereby realizing adaptive sparse representation. Then, we utilized SAStOMP to suppress strong electromagnetic interference and reconstruct useful MT signals. The technique was validated through simulated typical strong interference and measured MT data in ore district. The findings have proved that the proposed method can effectively eliminate large-scale strong interference and retain low-frequency useful signals in comparison with conventional methods such as remote reference (RR), orthogonal matching pursuit (OMP), and stage-wise orthogonal matching pursuit (StOMP). The obtained apparent resistivity-phase curve is smoother and more consistent, and the reflected underground electrical structure is more realistic and reliable.

Super‐resolution forward‐looking imaging method for manoeuvering platform with optimised dictionary and extended sparsity adaptive matching pursuit

In forward-looking imaging, left-right Doppler is ambiguous and cross-range resolution is limited by real aperture, which result in traditional synthetic aperture radar imaging methods no longer applicable. Besides, the impact of three-dimensional acceleration on an over-complete dictionary matrix and sparse reconstruction kernel is not considered in conventional super-resolution forward-looking imaging methods. To solve these problems, a super-resolution forward-looking imaging method for manoeuvering platforms is proposed. First, the range walk caused by forward-looking geometry and higher-order phase introduced by three-dimensional acceleration are eliminated by compensating a pre-processing function. Subsequently, according to beam steering-based geometry and linear regression model, the over-complete dictionary matrix is optimised to more accurately describe the complicated forward-looking geometry with curved trajectory. Finally, sparsity adaptive matching pursuit kernel with an improved halting condition is adopted to reconstruct the forward-looking scene. The proposed method is supported by point target simulation and surface target simulation.

SAR Imaging From Azimuth Missing Raw Data via Sparsity Adaptive StOMP

Synthetic aperture radar (SAR) raw data missing occurs when the radar is interrupted for various reasons during the work. Different solutions have been proposed to this problem. In recent years, with the continuous deepening of the research on compressed sensing (CS), it has also been fully utilized in solving the problem of missing data. When using traditional greedy algorithms to recover missing data, we need to know the sparsity, but it is often unknowable in practice. This letter proposes to apply the sparsity adaptive segmented orthogonal matching pursuit (SAStOMP) algorithm to the recovery of SAR missing data. Simulation results show that the proposed method can recover missing SAR data under the condition of unknown sparsity and can adapt to a wider range of threshold parameters. It has good recovery performance for periodic and nonperiodic missing SAR raw data, thus improving SAR imaging results.