Fast Sparse Bayesian Learning Research Articles

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.

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.

A Novel Fast Sparse Bayesian Learning STAP Algorithm for Conformal Array Radar

Space-time adaptive processing (STAP) is an important method of clutter suppression that requires adequate training samples. For an airborne conformal array radar, conventional STAP methods do not have enough training samples to acquire good performance due to the range dependent clutter caused by geometry and the problem of polarization. Sparse-recovery-based STAP (SR-STAP) methods have garnered significant attention in the past few decades because they only require a small number of training samples. Sparse Bayesian Learning (SBL) methods have seen increasing amounts of development due to its robust, self-regularizing nature and because it is not sensitive to user parameters, but it converges slowly. In this paper, a novel fast SBL (NFSBL) method is put forward to increase the rate of convergence. To minimize the SBL penalty function, the proposed method introduces the conjugate function to construct a surrogate function. Additional solution sparsity will be achieved through iteratively minimizing the surrogate function. Then, from the proposed method, we could obtain a more accurate clutter plus noise covariance matrix. Numerical simulation results express that this method could acquire better performance of STAP and improvement in convergence and computational complexity for a conformal array.

Efficient Implementation for SBL-Based Coherent Distributed mmWave Radar Imaging

In a distributed frequency-modulated continuous waveform (FMCW) radar system, the echo data collected are not continuous in the azimuth direction, so the imaging effect of the traditional range-Doppler (RD) algorithm is poor. Sparse Bayesian learning (SBL) is an optimization algorithm based on Bayesian theory that has been successfully applied to high-resolution radar imaging because of its strong robustness and high accuracy. However, SBL is highly computationally complex. Fortunately, with FMCW radar echo data, most of the time-consuming SBL operations involve a Toeplitz-block Toeplitz (TBT) matrix. In this article, based on this advantage, we propose a fast SBL algorithm that can be used to obtain high-angular-resolution images, in which the inverse of the TBT matrix can be transposed as the sum of the products of the block lower triangular Toeplitz matrix and the block circulant matrix by using a new decomposition method, and some of the matrix multiplications can be quickly computed using the fast Fourier transform (FFT), decreasing the computation time by several orders of magnitude. Finally, simulations and experiments were used to ensure the effectiveness of the proposed algorithm.

Sparse Aperture Autofocusing and Imaging Based on Fast Sparse Bayesian Learning From Gapped Data

Sparse aperture (SA) autofocusing and imaging is a hot research problem in the signal processing field and has been widely used. Under SA, the absence of echoes destroys the coherence between the pulses, which then affects the autofocusing accuracy of the imaging, leading to defocus of the image. In this paper, a novel SA autofocusing and imaging algorithm based on Sparse Bayesian Learning (SBL) is proposed, which uses a fast SBL algorithm to achieve SA high resolution imaging, and uses the minimum Tsallis entropy algorithm to realize autofocusing. As is known to all, SBL has strong robustness and high precision. Unfortunately, the direct calculation of the inversion and multiplication operations involved in each iteration of SBL results in significant computational costs. In the proposed fast SBL algorithm, the matrix required to be inverted has a special structure. The inverse matrix can then be represented by Gohberg-Semencul (G-S) factorization. And almost all operations except for G-S factorization during each iteration can be completed by fast Fourier transform (FFT) or inverse FFT (IFFT), which greatly reduces the amount of computation by several orders of magnitude. In each SBL iteration, the minimum Tsallis entropy algorithm is used for estimating the phase error, which has better noise sensitivity and obtains the images with the best focused degree. Finally, the effectiveness and high efficiency of the proposed fast algorithm are verified by experimental results obtained by simulation and measured data.

Underwater Acoustic Channel Estimation Based on Sparse Bayesian Learning Algorithm

The channel estimation algorithm based on sparse Bayesian learning proposed in recent years shows better performance than the traditional channel estimation algorithm by effectively reducing the convergence error in the channel estimation process. However, the sparse Bayesian learning algorithm based on expectation maximization (EM-SBL) is difficult to meet the practical applications with low complexity and power consumption. In order to guarantee the long-term stable communication of underwater devices, this paper proposes the fast sparse Bayesian learning algorithm based on Fast Marginal Likelihood Maximization (FM-SBL) to estimate underwater acoustic channels with low power consumption and high performance. Simulation and sea trial results show the output BER after channel estimation of FM-SBL is similar to that of EM-SBL, better than LS, MP and OMP, and it has good robustness in fast and slow time-varying channels. In terms of running speed, the FM-SBL algorithm is 16.7% of EM-SBL algorithm, which greatly reduces the estimation time.

Fast Sparse Bayesian Learning-Based Channel Estimation for Underwater Acoustic OFDM Systems

Harsh underwater channels and energy constraints are the two critical issues of underwater acoustic (UWA) communications. To achieve a high channel estimation performance under a severe underwater channel, sparse Bayesian learning (SBL)-based channel estimation was adopted for UWA orthogonal frequency division multiplexing (OFDM) systems. Accurate channel estimation can guarantee the successful reception of transmitted data and reduce retransmission occurrences, thereby, leading to energy-efficient communications. However, SBL-based algorithms have improved performances in iterative ways, which require high power consumption. In this paper, a fast SBL algorithm based on a weighted learning rule for hyperparameters is proposed for channel estimation in a UWA-OFDM system. It was shown via numerical analysis that the proposed weighted learning rule enables fast convergence and more accurate channel estimation simultaneously. Simulation results confirm that the proposed algorithm achieves higher accuracy in channel estimation with much fewer iteration numbers in comparison to conventional SBL-based methods for a time-varying UWA channel.

A fast sparse Bayesian learning method with adaptive Laplace prior for space‐time adaptive processing

Space-time adaptive processing with finite samples is supposed to be a crucial technique for airborne radar systems. Inspired by the application of Gaussian prior in sparse Bayesian learning algorithm and the adaptive least absolute shrinkage and selection operator algorithm, a hierarchical Bayesian framework with adaptive Laplace priors is proposed. In this paper, a novel method is applied to avoid the high-dimension matrix inverse operation in the proposed algorithm. Moreover, in order to apply the method in the complex-valued domain, the complex-valued signal is split into two independent variables. Then, the sparse recovery problem in the complex-valued domain can be transformed into the real-value domain. Simulation experiments show that the proposed algorithm can achieve great clutter suppression performance and also ensure high computational efficiency.

Bistatic inverse synthetic aperture radar sparse aperture self-focusing algorithm based on the joint constraint of compressed sensing and minimum Tsallias entropy

Based on the low imaging resolution of bistatic inverse synthetic aperture radar (Bi-ISAR) and the failure of pulse correlation under the condition of sparse aperture cause that of the traditional self-focusing algorithm, a Bi-ISAR sparse aperture self-focusing algorithm with the combined constraint of image quality optimization and sparsity is proposed. First, the proposed algorithm establishes the Bi-ISAR sparse aperture self-focusing signal model, reconstructs images through fast sparse Bayesian learning (FSBL), uses the minimum Tsallis entropy and constraints the reconstruction process, iteratively updates the phase error, and performs self-focusing to realize the initial phase correction of Bi-ISAR images. Simulation results show that the proposed algorithm has a fast convergence speed, strong robustness to noise, and high accuracy in reconstructing images.

Underdetermined wideband DOA estimation for off‐grid targets: a computationally efficient sparse Bayesian learning approach

Underdetermined wideband direction of arrival (DOA) estimation based on the sparse array is studied here and a novel algorithm is developed to improve the estimation performance of off-grid targets in the framework of sparse Bayesian learning. First, the narrowband off-grid model is extended to a wideband case and the sparse Bayesian model containing off-grid biases is deduced. Then, a sequential solution is proposed to obtain the estimation, where the fast sparse Bayesian learning strategy is employed to improve the computational efficiency. The estimation accuracy is improved significantly through off-grid compensation and the computational complexity is reduced remarkably. Simulation results verify the effectiveness of the proposed method.

Sparse Representation for Target Parameter Estimation in CDR-Based Passive Radar

In the China digital radio (CDR)-based passive radar, when the range-Doppler (RD) map is generated by the classical matched filtering method, the target range profile has the mainlobe splitting phenomenon. To solve this problem, we first derive the reason for the target mainlobe splitting from the subcarrier domain. Then, we develop an effective-subcarrier-based complex fast sparse Bayesian learning (ES-CFSBL) algorithm to generate RD map. Finally, simulation and experimental results show that the developed algorithm can effectively reduce sidelobe level and make it easier to detect and track weak targets covered by strong target sidelobes. Besides, the proposed method can realize fractional delay estimation conveniently.

Fast and robust Block-Sparse Bayesian learning for EEG source imaging

We propose a new Sparse Bayesian Learning (SBL) algorithm that can deliver fast, block-sparse, and robust solutions to the EEG source imaging (ESI) problem in the presence of noisy measurements. Current implementations of the SBL framework are computationally expensive and typically handle fluctuations in the measurement noise using different heuristics that are unsuitable for real-time imaging applications. We address these shortcomings by decoupling the estimation of the sensor noise covariance and the sparsity profile of the sources, thereby yielding an efficient two-stage algorithm. In the first stage, we optimize a simplified non-sparse generative model to get an estimate of the sensor noise covariance and a good initialization of the group-sparsity profile of the sources. Sources obtained at this stage are equivalent to those estimated with the popular inverse method LORETA. In the second stage, we apply a fast SBL algorithm with the noise covariance fixed to the value obtained in the first stage to efficiently shrink to zero groups of sources that are irrelevant for explaining the EEG measurements. In addition, we derive an initialization to the first stage of the algorithm that is optimal in the least squares sense, which prevents delays due to suboptimal initial conditions. We validate our method on both simulated and real EEG data. Simulations show that the method is robust to measurement noise and performs well in real-time, with faster performance than two state of the art SBL solvers. On real error-related negativity EEG data, we obtain source images in agreement with the experimental literature. The method shows promise for real-time neuroimaging and brain-machine interface applications.

Sparse Bayesian Learning with joint noise robustness and signal sparsity

This study concerns the issue of jointly enhancing noise robustness and promoting signal sparsity in Sparse Bayesian Learning (SBL), which aims at addressing the performance deficiency of sparse signal recovery due to uninformative data with low signal-to-noise ratios. In particular, the authors propose a hierarchical prior noise model with a signal-dependent parametrisation and incorporate it into developing the robust SBL algorithms for sparse signal recovery. The main contribution of the proposed approach is twofold. The first is the new consideration of noise-robustness enhancement in building SBL algorithms, which devotes to noise awareness in counteracting outliers in measurements. Specifically, the idea of signal-sparsity enforcing is extended to build a Least Absolute Deviation like loss criterion with the proposed hierarchical prior model of measurement noise. The second is the novelty of using the signal-dependent parametrisation in the proposed noise model. Indeed, the signal-dependent mechanism plays an indispensable role in producing the reliable noise parameter estimation jointly with updating signal model parameters under the fast SBL framework. In addition to numerical simulation studies, the real-life application of radio tomographic imaging is presented to validate the proposed approach.

Coherent Processing and Superresolution Technique of Multi-Band Radar Data Based on Fast Sparse Bayesian Learning Algorithm

The coherent processing and superresolution of multi-band radar data from multiple spatially collocated radars is addressed by utilizing a sparse representation technique in this paper. Firstly a parametric model based on geometrical theory of diffraction (GTD) is adopted to construct a redundant dictionary and provide a good match to the scattering mechanism. Then weights of dictionary atoms are computed by using a fast sparse Bayesian learning algorithm. Meanwhile, a multilevel dynamic dictionary is proposed to improve the accuracy and avoid a vast number of computations due to a large dictionary matrix. The final weights and dictionary atoms are adopted to interpolate between and extrapolate outside of the measurement subbands. Furthermore, a procedure for coherent processing is presented to compensate for the lack of mutual coherence among multiband data from multiple spatially collocated radars. The capability and robustness of the proposed method are validated by applying it to the analytical, simulated and static-range data.