Sparse Bayesian Learning Algorithm Research Articles

A TMSBL underwater acoustic channel estimation method based on dictionary learning denoising

The shallow sea underwater acoustic channel exhibits a significant sparse multipath structure. The temporally multiple sparse Bayesian learning (TMSBL) algorithm can effectively estimate this sparse multipath channel. However, the complexity of the algorithm is high, the signal-to-noise ratio (SNR) of shallow-sea underwater acoustic communication is low, and the estimation performance of the TMSBL algorithm is greatly affected by noise. To address this problem, an improved TMSBL underwater acoustic channel estimation method based on a dictionary learning noise reduction algorithm is proposed. Firstly, the K-Singular Value Decomposition (K-SVD) dictionary learning method is used to reduce the noise of the received pilot matrix, reducing the influence of noise on the signal. Then, the Generalized Orthogonal Matching Pursuit (GOMP) channel estimation method is combined to obtain a priori information such as the perceptual matrix and hyperparameter matrix for TMSBL channel estimation; and the noise variance is obtained by using the null subcarrier calculation instead of iteratively updating the noise variance in the TMSBL, to improve the estimation accuracy and reduce the algorithmic complexity. Finally, the TMSBL channel estimation method is used to estimate the underwater acoustic channels of different symbols jointly. The simulation results show that the normalized mean square error of the channel estimation of the improved TMSBL method is reduced by about 92.2% compared with the TMSBL algorithm, obtaining higher estimation accuracy; running time is reduced by about 45.6%, and there is also better performance in terms of the running speed, which provides a reference for underwater acoustic channel estimation.

Improving Quantitative Analysis with Cross Instrument-Sparse Bayesian Learning (CI-SBL) Raman Spectroscopy Analysis Algorithm.

Qualitative and quantitative analysis of Raman spectroscopy is a widely used nondestructive analytical technique in many fields. It utilizes the Raman scattering effect of lasers to obtain molecular vibration information on samples. By comparison with the Raman spectra of standard substances, qualitative and quantitative analyses can be achieved on unknown samples. However, current Raman spectroscopy analysis algorithms still have many drawbacks. They struggled to handle quantitative analysis between different instruments. Their prediction accuracy for concentration is generally low, with poor robustness. Therefore, this study addresses these deficiencies by designing the cross instrument-sparse Bayesian learning (CI-SBL) Raman spectroscopy analysis algorithm. CI-SBL can facilitate spectroscopic analysis between different instruments through the cross instrument module. CI-SBL converts data from portable instruments into data from scientific instruments, with high similarity between the converted spectrum and the spectrum from the scientific instruments reaching 98.6%. The similarity between the raw portable instrument spectrum and the scientific instrument spectrum is often lower than 90%. The cross instrument effect of the CI-SBL is remarkable. Moreover, CI-SBL employs sparse Bayesian learning (SBL) as the core module for analysis. Through multiple iterations, the SBL algorithm effectively identified various components within mixtures. In experiments, CI-SBL can achieve a qualitative accuracy of 100% for the majority of binary and multicomponent mixtures. On the other hand, the previous Raman spectroscopy analysis algorithms predominantly yield a qualitative accuracy below 80% for the same data. Additionally, CI-SBL incorporates a quantitative module to calculate the concentration of each component within the mixed samples. In the experiment, the quantification error for all substances was below 3%, with the majority of the substances exhibiting an error of approximately 1%. These experimental results illustrate that CI-SBL significantly enhances the accuracy of qualitative judgment of mixture spectra and the prediction of mixture concentrations compared with previous Raman spectroscopy analysis algorithms. Furthermore, the cross instrument module of CI-SBL allows for a flexible handling of data acquired from different instruments.

Knowledge-aided multi-dictionary block sparsity-aware STAP for airborne polarimetric conformal array radar

Airborne polarimetric conformal array radar has gained increased attention recently. However, the conformal array configuration and polarization factors may lead to non-stationary clutter, which significantly degrades the performance of space–time adaptive processing (STAP), particularly in short-range clutter environments. In this paper, we introduce a knowledge-aided multi-dictionary block sparse Bayesian learning (KA-MDBSBL) algorithm to improve the clutter suppression performance. Using prior knowledge, the proposed algorithm designs multi-dictionary matrices for each training sample, rather than a single dictionary matrix for the cell under test (CUT). We take advantage of the identical clutter profile under each dictionary matrix. In the multi-dictionary case, we enforce shared sparsity in the clutter profiles. Additionally, we utilize the inherent block structure of the dictionary matrix to jointly recover clutter and noise power through a fast convergence learning framework. Subsequently, the clutter plus noise covariance matrix is reconstructed using precisely estimated clutter and noise power, along with the dictionary matrix corresponding to the CUT. Numerical simulations are included to demonstrate the effectiveness and superiority of the proposed algorithm.

Airborne Radar Space–Time Adaptive Processing Algorithm Based on Dictionary and Clutter Power Spectrum Correction

Sparse recovery space–time adaptive processing (SR-STAP) technology improves the moving target detection performance of airborne radar. However, the sparse recovery method with a fixed dictionary usually leads to an off-grid effect. This paper proposes a STAP algorithm for airborne radar based on dictionary and clutter power spectrum joint correction (DCPSJC-STAP). The algorithm first performs nonlinear regression in a non-stationary clutter environment with unknown yaw angles, and it corrects the corresponding dictionary for each snapshot by updating the clutter ridge parameters. Then, the corrected dictionary is combined with the sparse Bayesian learning algorithm to iteratively update the required hyperparameters, which are used to correct the clutter power spectrum and estimate the clutter covariance matrix. The proposed algorithm can effectively overcome the off-grid effect and improve the moving target detection performance of airborne radar in actual complex clutter environments. Simulation experiments verified the effectiveness of this algorithm in improving clutter estimation accuracy and moving target detection performance.

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.

A High-Resolution Time Reversal Method for Target Localization in Reverberant Environments

Reverberation in real environments is an important factor affecting the high resolution of target sound source localization (SSL) methods. Broadband low-frequency signals are common in real environments. This study focuses on the localization of this type of signal in reverberant environments. Because the time reversal (TR) method can overcome multipath effects and realize adaptive focusing, it is particularly suitable for SSL in a reverberant environment. On the basis of the significant advantages of the sparse Bayesian learning algorithm in the estimation of wave direction, a novel SSL is proposed in reverberant environments. First, the sound propagation model in a reverberant environment is studied and the TR focusing signal is obtained. We then use the sparse Bayesian framework to locate the broadband low-frequency sound source. To validate the effectiveness of the proposed method for broadband low-frequency targeting in a reverberant environment, simulations and real data experiments were performed. The localization performance under different bandwidths, different numbers of microphones, signal-to-noise ratios, reverberation times, and off-grid conditions was studied in the simulation experiments. The practical experiment was conducted in a reverberation chamber. Simulation and experimental results indicate that the proposed method can achieve satisfactory spatial resolution in reverberant environments and is robust.

Beam-Space Post-Doppler Reduced-Dimension STAP Based on Sparse Bayesian Learning

The space–time adaptive processing (STAP) technique can effectively suppress the ground clutter faced by the airborne radar during its downward-looking operation and thus can significantly improve the detection performance of moving targets. However, the optimal STAP requires a large number of independent identically distributed (i.i.d) samples to accurately estimate the clutter plus noise covariance matrix (CNCM), which limits its application in practice. In this paper, we fully consider the heterogeneity of clutter in real-world environments and propose a sparse Bayesian learning-based reduced-dimension STAP method that achieves suboptimal clutter suppression performance using only a single sample. First, the sparse Bayesian learning (SBL) algorithm is used to estimate the CNCM using a single training sample. Second, a novel angular Doppler channel selection algorithm is proposed with the criterion of maximizing the output signal-to-clutter-noise ratio (SCNR). Finally, the reduced-dimension STAP filter is constructed using the selected channels. Simulation results show that the proposed algorithm can achieve suboptimal clutter suppression performance in extremely heterogeneous clutter environments where only one training sample can be used.

High-Throughput MPSoC Implementation of Sparse Bayesian Learning Algorithm

In the field of sparse signal reconstruction, sparse Bayesian learning (SBL) has excellent performance, which is accompanied by extremely high computational complexity. This paper presents an efficient SBL hardware and software (HW&SW) co-implementation method using the ZYNQ series MPSoC (multiprocessor system-on-chip). Firstly, considering the inherent challenges in parallelizing iterative algorithms like SBL, we propose an architecture based on the iterative calculations implemented on the PL side (FPGA) and the iteration control and input management handled by the PS side (ARM). By adopting this structure, we can take advantage of task-level pipelines on the FPGA side, effectively utilizing time and space resources. Secondly, we utilize LDL decomposition to perform the inversion of the Hermitian matrix, which not only exhibits the lowest computational complexity and requires fewer computational resources but also achieves a higher level in the parallel pipeline mechanism compared with other alternative methods. Furthermore, the algorithm conducts iterations sequentially, utilizing the parameters derived from the previous dataset as prior information for initializing the subsequent dataset’s initial values. This approach helps to reduce the number of iterations required. Finally, with the help of Vitis HLS 2022.2 and Vivado tools, we successfully accomplished the development of a hardware design language and its implementation on the ZYNQ UltraScale+ MPSoC ZCU102 platform. Meanwhile, we have solved a direction of arrival (DOA) estimation problem using horizontal line arrays to verify the practical feasibility of the method.

Sparse Bayesian learning based on spatio-temporal structure-aware for matched field processing.

In the application of the matched field processing (MFP) algorithm for underwater acoustic source localization, the measurements at each time step are conventionally processed independently. This study incorporates the prior information about the continuous spatial changes of the source over time under realistic conditions, a factor anticipated to improve localization performance. In this paper, a sparse Bayesian learning (SBL) algorithm based on the spatio-temporal structure-aware is described. We exploit a structure prior for sparse coefficients to capture the continuous spatial structure between adjacent time steps. Moreover, the sparse coefficient can automatically select the update method, utilizing the statistical information from adjacent neighbors or updating independently. The hidden variables in the hierarchical Bayesian framework are inferred via variational Bayesian inference (VBI). Additionally, we extend the proposed method to the multi-frequency case. This method inherits the advantages of the SBL and further reduces position estimation errors. Compared to other approaches, the construction of an accurate motion model is not required. The efficacy of the proposed algorithm is demonstrated through simulation examples and an analysis of the SWellEx-96 experimental data.

Sparse Bayesian Learning for Switching Network Identification.

Learning dynamical networks based on time series of nodal states is of significant interest in systems science, computer science, and control engineering. Despite recent progress in network identification, most research focuses on static structures rather than switching ones. Therefore, this article develops a method for identifying the structures of switching networks by exploring and leveraging both temporal and spatial structural information that characterizes the switching process. The proposed method employs a new sparse Bayesian learning algorithm based on coupled hyperblocks to estimate unknown switching instants. Experimental results on benchmark artificial and real networks are elaborated to demonstrate the effectiveness and superiority of the proposed method.

Fast sparse Bayesian learning-based seismic resolution enhancement

Seismic high resolution processing plays a crucial role in seismic interpretation and reservoir characterization. However, the low and high frequency of seismic signal are lost owing to the effects of earth filtering and diffraction. The missing of low-frequency increases the energy of wavelet side lobe, which not only enhances the interference with adjacent events, but also lead to side lobe artifacts. High frequency attenuation is more serious, which significantly reduces the seismic resolution. In addition, the current resolution enhancement methods are difficult to achieve desirable result in noise contaminated environment. A novel resolution enhancement method that extends high and low frequencies simultaneously and improves the signal-to-noise ratio (SNR) under the framework of sparse decomposition theory is proposed. Firstly, an over-complete dictionary is constructed using non-zero phase Ricker wavelet and then the effective seismic signal is extracted by sparse decomposition using the fast sparse Bayesian learning (FSBL) algorithm. Secondly, the effective frequency range of the seismic signal is determined through a series of atoms obtained by sparse decomposition. Then, a desired broadband spectrum can be identified depending on this range. By approximating the broadband spectrum of seismic data, the weak high-frequency information can be extended. Furthermore, a correction term is introduced in frequency domain to suppress the side lobes of atoms. The side lobes are well suppressed without distorting the main lobe, meanwhile, both the low and high frequencies are extended. Finally, the validity of this method is verified by synthetic and field data. The results show that this method has better performance than the ordinary deconvolution and spectral whitening methods in processing high resolution data.

Deep Unfolding Sparse Bayesian Learning Network for Off-Grid DOA Estimation with Nested Array

Recently, deep unfolding networks have been widely used in direction of arrival (DOA) estimation because of their improved estimation accuracy and reduced computational cost. However, few have considered the existence of a nested array (NA) with off-grid DOA estimation. In this study, we present a deep sparse Bayesian learning (DSBL) network to solve this problem. We first establish the signal model for off-grid DOA with NA. Then, we transform the array output into a real domain for neural networks. Finally, we construct and train the DSBL network to determine the on-grid spatial spectrum and off-grid value, where the loss function is calculated using reconstruction error and the sparsity of network output, and the layers correspond to the steps of the sparse Bayesian learning algorithm. We demonstrate that the DSBL network can achieve better generalization ability without training labels and large-scale training data. The simulation results validate the effectiveness of the DSBL network when compared with those of existing methods.

Joint channel and impulse noise estimation based on compressed sensing and Kalman filter for OFDM system

Impulse noise (IN) widely exists in many communication systems, which seriously affects the performance of OFDM communication systems. A joint channel and IN estimation method based on all subcarriers is designed. This method uses a sparse Bayesian learning (SBL) algorithm incorporating forward–backward Kalman filter (FB-Kalman) to tackle the problem of joint channel and IN estimation and data detection for OFDM systems. Firstly, the channel impulse response and IN are regarded as unknown sparse vectors, and a SBL framework using all subcarriers is proposed to estimate the unknown vector. The SBL theory is used based on the prior distribution of variables, and then the forward–backward joint system is established, which applies the data detection simultaneously. We also propose the FB-Kalman implementation algorithm by using the expectation maximization updates. Explicit expressions of mean and covariance matrix of the posterior distribution are derived in the E-step. Simulation results show that the proposed algorithm improves the normalized mean square error and bit error rate performance of OFDM system in the presence of IN communication environment.

Low complexity joint angle and delay estimation for underwater multipath acoustic channel based on sparse Bayesian learning

In the field of underwater acoustic communication, multipath signals arrive at the receiving end with different angles and path delays, which can cause degradation in communication quality. When performing angle-delay joint estimation, sparse Bayesian learning (SBL) has many advantages over traditional methods, such as high accuracy, resolution and global minimum results, but at the cost of high computational complexity. Regarding this, in this study, we propose a low-complexity SBL based framework to jointly estimate the angle and delay of the received signal. We first propose a low-complexity approximation SBL algorithm applied to joint estimation, which can keep the super-resolution and estimation accuracy but significantly reduce the computation time. To further tackle the problem of performance degradation of the approximate algorithm in underwater low signal-to-noise ratio environments, we utilize above result as a starting point for the space-alternating generalized Expectation Maximization (SAGE) algorithm to achieve a more precise estimation. Simulation and experimental results demonstrate that the proposed algorithm has an excellent performance in various underwater multipath scenarios.

High-resolution on-chip spatial heterodyne Fourier transform spectrometer based on artificial neural network and PCSBL reconstruction algorithm.

A novel compact on-chip Fourier transform (FT) spectrometer has been proposed based on the silicon-on-insulator (SOI) platform with wide operating bandwidth and high resolution. The spectrometer consists of a 16-channel power splitter and a Mach-Zehnder interferometer (MZI) array of 16 MZIs with linearly increasing optical path length (OPL) difference. We have also developed a spectral retrieval algorithm based on the pattern-coupled sparse Bayesian learning (PCSBL) algorithm and artificial neural network (ANN). The experimental results show that the designed spectrometer has a flat transmission characteristic in the wavelength range between 1500 nm and 1600 nm, indicating that the device has a wide operating bandwidth of 100 nm. In addition, with the assistance of the spectral retrieval algorithm, our spectrometer has the ability to reconstruct narrowband signals with full width at half maximum (FWHM) of 0.5 nm and a triple-peaked signal separated by a 3-nm distance.

Bayesian adaptive beamformer for robust electromagnetic brain imaging of correlated sources in high spatial resolution.

Reconstructing complex brain source activity at a high spatiotemporal resolution from magnetoencephalography (MEG) or electroencephalography (EEG) remains a challenging problem. Adaptive beamformers are routinely deployed for this imaging domain using the sample data covariance. However adaptive beamformers have long been hindered by 1) high degree of correlation between multiple brain sources, and 2) interference and noise embedded in sensor measurements. This study develops a novel framework for minimum variance adaptive beamformers that uses a model data covariance learned from data using a sparse Bayesian learning algorithm (SBL-BF). The learned model data covariance effectively removes influence from correlated brain sources and is robust to noise and interference without the need for baseline measurements. A multiresolution framework for model data covariance computation and parallelization of the beamformer implementation enables efficient high-resolution reconstruction images. Results with both simulations and real datasets indicate that multiple highly correlated sources can be accurately reconstructed, and that interference and noise can be sufficiently suppressed. Reconstructions at 2-2.5mm resolution (~150K voxels) are possible with efficient run times of 1-3 minutes. This novel adaptive beamforming algorithm significantly outperforms the state-of-the-art benchmarks. Therefore, SBL-BF provides an effective framework for efficiently reconstructing multiple correlated brain sources with high resolution and robustness to interference and noise.

Sound source identification using the boundary element method in a sparse framework

Traditional near-field acoustic holography (NAH) based on the boundary element method (BEM) exhibits good performance for sound source identification. However, good reconstruction results can only be guaranteed if a sufficient number of sampling points are used. In this paper, the unitary matrix is used as the sparse basis matrix of source surface velocity and is obtained from the transfer matrix between the source surface sound pressure and vibration velocity by singular value decomposition (SVD). Based on this sparse basis, a sparse Bayesian learning (SBL) algorithm is introduced into BEM-based NAH to address the case of few sampling points. The use of a standard SBL algorithm in BEM-based NAH leads to hyperparameters that are overly sparse due to the large number of iterations, which results in large reconstruction errors. To solve this problem, a modified SBL algorithm is proposed. Good reconstruction results are maintained by selecting appropriate hyperparameters and revising the results using the steepest descent method. A simulated cuboid shell is used to explore the influence of the (i) number of sampling points and (ii) signal-to-noise ratio (SNR) on the reconstruction. Numerical results show that the proposed method can achieve effective reconstruction when the number of sampling points is approximately one-tenth of the number of discrete points on the source surface. The validity of the proposed method is verified by a comparison with experimental results.

High-Speed Maneuvering Target Inverse Synthetic Aperture Radar Imaging and Motion Parameter Estimation Based on Fast Spare Bayesian Learning and Minimum Entropy

High-speed maneuvering target inverse synthetic aperture radar (ISAR) imaging is always a hot topic in signal processing. High-speed maneuvering targets often have high-order maneuvering characteristics, such as translational and rotational characteristics, which destroy the signal structure of stationary targets and make basic imaging processing methods such as range-Doppler (RD) algorithm no longer suitable. In this paper, a high-resolution imaging method for high-speed maneuvering targets is proposed, which uses the fast sparse Bayesian learning (SBL) algorithm and the minimum entropy algorithm for ISAR high-resolution imaging and motion parameter estimation, respectively. Because SBL makes full use of the characteristics of the target and the environment, it can obtain an ISAR high-resolution image of the maneuvering target. However, the high computational complexity caused by matrix inversion and some matrix operations in SBL iteration limit the practical application of SBL in ISAR imaging. In view of the special structure of the matrix required to be inverted, we propose a fast SBL algorithm, which uses a new decomposition method to obtain the decomposition formula of the inverse matrix. Based on the decomposition factors, the multiplication operation involving the inverse matrix can be quickly calculated using fast Fourier transform (FFT), which greatly improves the computational efficiency. Image entropy represents the sharpness and focusing degree of an image, and so the minimum entropy algorithm can estimate the motion parameters of maneuvering targets more accurately. We combine the minimum entropy algorithm with the fast SBL algorithm to realize phase error correction and high-resolution imaging, which has better noise sensitivity and can obtain the best focusing degree image. Finally, simulation results prove the effectiveness of this algorithm.

Deep Learning-Based Channel Estimation for Wideband Hybrid MmWave Massive MIMO

Hybrid analog-digital (HAD) architecture is widely adopted in practical millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems to reduce hardware cost and energy consumption. However, channel estimation in the context of HAD is challenging due to only limited radio frequency (RF) chains at transceivers. Although various compressive sensing (CS) algorithms have been developed to solve this problem by exploiting inherent channel sparsity and sparsity structures, practical effects, such as power leakage and beam squint, can still make the real channel features deviate from the assumed models and result in performance degradation. Besides, the high complexity of CS algorithms caused by a large number of iterations hinders their applications in practice. To tackle these issues, we develop a deep learning (DL)-based channel estimation approach where the sparse Bayesian learning (SBL) algorithm is unfolded into a deep neural network (DNN). In each SBL layer, Gaussian variance parameters of the sparse angular domain channel are updated by a tailored DNN, which is able to capture complicated channel sparsity structures in various domains effectively and efficiently. The measurement matrix is jointly optimized for performance improvement. Then, the proposed approach is extended to the multi-block case where channel correlation in time is further exploited to adaptively predict the measurement matrix and facilitate the update of variance parameters. Simulation results show that the proposed approaches outperform existing approaches in terms of both performance and complexity.

Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.