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Mu rhythm is a spontaneous neural response occurring during a motor imagery (MI) task and has been increasingly applied to the design of brain–computer interface (BCI). Accurate classification of MI is usually rather difficult to be achieved since mu rhythm is very weak and likely to be contaminated by other background noises. As an extension of the single layer feedforward network, extreme learning machine (ELM) has recently proven to be more efficient than support vector machine that is a benchmark for MI-related EEG classification. With probabilistic inference, this study introduces a sparse Bayesian ELM (SBELM)-based algorithm to improve the classification performance of MI. SBELM is able to automatically control the model complexity and exclude redundant hidden neurons by combining advantageous of both ELM and sparse Bayesian learning. The effectiveness of SBELM for MI-related EEG classification is validated on a public dataset from BCI Competition IV IIb in comparison with several other competing algorithms. Superior classification accuracy confirms that the proposed SBELM-based algorithm is a promising candidate for performance improvement of an MI BCI.

Sparse Bayesian learning (SBL) is widely applied in direction‐of‐arrival (DOA) estimation. However, it is limited by complexity, grid mismatch and inappropriate initial values of noise. To address these problems, a DOA estimation algorithm using grid pruning and adaptation based on noise integral‐based sparse Bayesian learning (AGNISBL) method is proposed in this letter. To reduce complexity, grid pruning is introduced for expectation maximization (EM) framework. Furthermore, a novel adaptive‐grid method is proposed for solving grid mismatch. A noise integral‐based inference framework is used to improve the robustness of the sparse Bayesian method. Simulation results show that the performance of the proposed AGNISBL approaches CRB at high signal‐to‐noise ratios (SNR) and with lower time complexity compared to other methods.

Thin-walled parts such as blades are widely used in aerospace field, and their machining quality directly affects the service performance of core components. Due to obvious time-varying nonlinear effect and complex machining system, it is a great challenge to realize accurate and fast prediction of machining errors of such parts. To solve the above problems, an engineering knowledge based sparse Bayesian learning approach is proposed to realize in-situ prediction of machining errors of thin-walled blades. Firstly, an engineering knowledge based strategy is proposed to improve the generalization ability of the model by integrating multi-source engineering knowledge, including machining information, physical information and online monitoring information. Then, principal component analysis method is utilized for the dimensional reduction of features. Sparse Bayesian learning approach is developed for model training, which significantly reduce the complexity of the regression model. Finally, the superiority and effectiveness of the proposed approach have been proven in blade milling experiments. Experimental results show that the average deviation of the proposed in-situ prediction model is about 11 μm, and the model complexity is reduced by 66%.

Single-image super-resolution (SISR) continues to face difficulties in reconstructing perceptually critical details from degraded low-resolution observations. While conventional Bayesian approaches utilizing Relevance Vector Machines (RVMs) provide probabilistic interpretations, their reliance on fixed blur kernel definitions and homogeneous pixel dependency models often yields artifacts in complex scenarios. To resolve these issues, this study introduces a hierarchical Bayesian architecture enhanced by an adaptive Laplacian prior, which extends the sparse Bayesian learning (SBL) paradigm. Diverging from traditional Gaussian-based frameworks, our method employs sparsity-inducing regularization to selectively prioritize structurally salient regions (e.g., edge discontinuities, texture boundaries), while dynamically quantifying reconstruction uncertainty through pixel-wise variance analysis. Additionally, a spatially adaptive optimization mechanism is designed to streamline computational workflows without compromising restoration fidelity. Evaluations across multiple benchmarks confirm the framework’s advantages: it surpasses existing state-of-the-art techniques in both quantitative metrics (PSNR, SSIM) and qualitative assessments, demonstrating superior artifact suppression in high-frequency domains. Comparative analyses against recent state-of-the-art models further validate its capability to harmonize sparse representation with structural coherence.

Obtaining accurate angle parameters using direction-of-arrival (DOA) estimation algorithms is crucial for acquiring channel state information (CSI) in massive multiple-input multiple-output (MIMO) systems. However, the performance of the existing algorithms deteriorates severely due to mutual coupling between antenna elements in practical engineering. Therefore, for solving the array mutual coupling, the array output signal vector is modeled by mutual coupling coefficients and the DOA estimation problem is transformed into block sparse signal reconstruction and parameter optimization in this paper. Then, a novel sparse Bayesian learning (SBL)-based algorithm is proposed, in which the expectation-maximum (EM) algorithm is used to estimate the unknown parameters iteratively, and the convergence speed of the algorithm is enhanced by utilizing the approximate approximation. Moreover, considering the off-grid error caused by discretization processes, the grid refinement is carried out using the polynomial roots to realize the dynamic update of the grid points, so as to improve the DOA estimation accuracy. Simulation results show that compared with the existing algorithms, the proposed algorithm is more robust to mutual coupling and off-grid error and can obtain better estimation performance.

For direction-of-arrival (DOA) estimation problems in a sparse domain, sparse Bayesian learning (SBL) is highly favored by researchers owing to its excellent estimation performance. However, traditional SBL-based methods always assign Gaussian priors to parameters to be solved, leading to moderate sparse signal recovery (SSR) effects. The reason is Gaussian priors play a similar role to l2 regularization in sparsity constraint. Therefore, numerous methods are developed by adopting hierarchical priors that are used to perform better than Gaussian priors. However, these methods are in straitened circumstances when multiple measurement vector (MMV) data are adopted. On this basis, a block-sparse SBL method (named BSBL) is developed to handle DOA estimation problems in MMV models. The novelty of BSBL is the combination of hierarchical priors and block-sparse model originating from MMV data. Therefore, on the one hand, BSBL transfers the MMV model to a block-sparse model by vectorization so that Bayesian learning is directly performed, regardless of the prior independent assumption of different measurement vectors and the inconvenience caused by the solution of matrix form. On the other hand, BSBL inherited the advantage of hierarchical priors for better SSR ability. Despite the benefit, BSBL still has the disadvantage of relatively large computation complexity caused by high dimensional matrix operations. In view of this, two operations are implemented for low complexity. One is reducing the matrix dimension of BSBL by approximation, generating a method named BSBL-APPR, and the other is embedding the generalized approximate message passing (GAMB) technique into BSBL so as to decompose matrix operations into vector or scale operations, named BSBL-GAMP. Moreover, BSBL is able to suppress temporal correlation and handle wideband sources easily. Extensive simulation results are presented to prove the superiority of BSBL over other state-of-the-art algorithms.

Through extensive literature review, it has been found that sparse Bayesian learning (SBL) is mainly applied to traditional scalar hydrophones and is rarely applied to vector hydrophones. This article proposes a direction of arrival (DOA) estimation method for vector hydrophones based on SBL (Vector-SBL). Firstly, vector hydrophones capture both sound pressure and particle velocity, enabling the acquisition of multidimensional sound field information. Secondly, SBL accurately reconstructs the received vector signal, addressing challenges like low signal-to-noise ratio (SNR), limited snapshots, and coherent sources. Finally, precise DOA estimation is achieved for multiple sources without prior knowledge of their number. Simulation experiments have shown that compared with the OMP, MUSIC, and CBF algorithms, the proposed method exhibits higher DOA estimation accuracy under conditions of low SNR, small snapshots, multiple sources, and coherent sources. Furthermore, it demonstrates superior resolution when dealing with closely spaced signal sources.

Digital predistortion and nonlinear behavioral modeling of power amplifiers (PA) have been the subject of intensive research in the time domain (TD), in contrast with the limited number of works conducted in the frequency domain (FD). However, the adoption of orthogonal frequency division multiplexing (OFDM) as a prevalent modulation scheme in current wireless communication standards provides a promising avenue for employing an FD approach. In this work, a procedure to model nonlinear distortion in wireless OFDM systems in the frequency domain is demonstrated for general model structures based on a sparse Bayesian learning (SBL) algorithm to identify a reduced set of regressors capable of an efficient and accurate prediction. The FD-SBL algorithm is proposed to first identify the active FD regressors and estimate the coefficients of the PA model using a given symbol, and then, the coefficients are employed to predict the distortion of successive OFDM symbols. The performance of this proposed FD-SBL with a validation NMSE of −47 dB for a signal of 30 MHz bandwidth is comparable to −46.6 dB of the previously proposed implementation of the TD-SBL. In terms of execution time, the TD-SBL fails due to excessive processing time and numerical problems for a 100 MHz bandwidth signal, whereas the FD-SBL yields an adequate validation NMSE of −38.6 dB.

To solve the poor performance or even failure of the cross-spectrum (CS) method in hydroacoustic weak-target passive velocimetry, a sparse Bayesian learning cross-spectrum method (SBL-CS), combining phase compensation with sparse Bayesian learning (SBL) is proposed in this paper. Firstly, the cross-correlation sound intensity is taken as the observation quantity and compensates for each frequency point of the cross-spectrum, which enables the alignment of cross-spectrum results at different frequencies. Then, the inter-correlation sound intensity of all frequencies is fused in the iterative estimation of the target velocity, verifying the proposed method’s ability to suppress the background noise when performing multi-frequency processing. The simulation results show that the proposed method is still effective in estimating the target velocity when the CS method fails and that the performance of the proposed method is better than the CS method with a decrease in SNR. As verified using the SWellEx-96 sea trial dataset, the RMSE of the proposed method for surface vessel speed measurement is 0.3545 m/s, which is 46.1% less than the traditional CS method, proving the feasibility and effectiveness of the proposed SBL-CS method for the estimation of the radial speed of a passive target.

For the traditional uniform linear array (ULA) direction of arrival (DOA) estimation method with a limited array aperture, a non-circular signal off-grid sparse Bayesian DOA estimation method based on nested arrays is proposed. Firstly, the extended matrix of the received data is constructed by taking advantage of the fact that the statistical properties of non-circular signals are not rotationally invariant. Secondly, we use the difference and sum co-arrays for the nested array technique, thus increasing the array aperture and improving the estimation accuracy. Finally, we take the noise as part of the interest signal and iteratively update the grid points using the sparse Bayesian learning (SBL) method to eliminate the modeling errors caused by off-grid gaps. The simulation results show that the proposed algorithm can improve the accuracy of DOA estimation compared with the existing algorithms.