Robust multi-frequency sparse Bayesian learning: Theory and simulations

Sparse Bayesian learning for the Laplace transform inversion in dynamic light scattering

We consider the progressive reconstruction of a streaming signal from compressive, streaming measurements. We develop a progressive reconstruction algorithm based on sliding window processing, where we reconstruct the streaming signal over small overlapping shifting intervals. Since the consecutive intervals share some common sparse signal vectors, the key idea of this work is to utilize the preliminary information from the preceding interval to improve the performance of the signal recovery algorithm. For this purpose, we propose a novel sparse Bayesian learning (SBL) algorithm, which is highly efficient for recovering streaming signals. One major advantage of SBL is that it provides a measure of uncertainty of the reconstructed signal rather than computing only a point estimate. The proposed SBL algorithm utilizes the previous estimates as well as the correlations among the nonzero coefficients to improve the performance of the algorithm. Since the effect of uncertainty of the reconstructed signal from the preceding interval is specifically taken into account in the recovery process of the current interval, the proposed algorithm is more robust to the error propagation compared to the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm minimization counterpart. Further, we propose a warm-start procedure and derive fast update formulae to reduce the computational cost of the SBL algorithm. In addition, we also discuss the properties of the signal and the underlying approximations which enable the progressive reconstruction of the streaming signal from compressive measurements.

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.

Scalable and memory-efficient sparse learning for classification with approximate Bayesian regularization priors

Underwater acoustic channels typically exhibit clustered-sparse structure, and sparse channel recovery based on the clustered-sparse structure can achieve smaller structural error. We propose a novel clustered-sparse Bayesian model for sparse channel estimation in underwater acoustic (UWA) orthogonal frequency-division multiplexing (OFDM) communication systems. In this model, the sparsity and temporal correlation of channel impulse responses (CIRs) are controlled by a set of hyperparameters. For continuously transmitted OFDM blocks in one frame, the auto-regressive (AR) process is used to characterize temporal correlation of time-varying UWA channels, and different clusters are considered to have different AR model coefficients, as they are usually generated according to different transmission routes. A joint cluster partition and sparse Bayesian learning algorithm (JCP-SBL) is proposed to learn the clustered-sparse structure of UWA channels when the cluster partition is unknown. Results of numerical simulation and lake trial demonstrate the effectiveness of the JCP-SBL channel estimator in time-varying UWA channel, which achieve better channel estimation performance and lower bit error rate (BER) compared with the orthogonal matching pursuit (OMP), simultaneous OMP (SOMP) and temporal multiple sparse Bayesian learning (TMSBL).

In this article we study the sparse signal recovery problem in a Bayesian framework using a novel Bootstrapped Sparse Bayesian Learning method. Sparse Bayesian Learning (SBL) framework is an effective tool for pruning out the irrelevant features and ending up with a sparse representation. In SBL the choice of prior over the variances of the Gaussian Scale mixture has been an interesting area of research for some time now. This motivates us to use a more generalized maximum entropy density as the prior which results in a new variant of SBL. It has been shown to perform better than traditional SBL empirically and it also accelerates the pruning procedure. Because of this advantage, this variant of SBL can be claimed as more robust choice as it is less sensitive to the threshold for pruning. Theoretical justifications have also been provided to show that the proposed model actually promotes sparse point estimates.

Channel estimation is crucial to beamforming techniques in directional millimetre wave (mmWave) communications, which is generally designed based on channel state information static. However, due to the Doppler effect caused by the mobility of users, such as unmanned aerial vehicles, high-speed trains and autonomous vehicles, the mmWave channel is changing rapidly. Spatial channel covariance, defined by long-term statistic information of channels, is a promising solution to reduce channel estimation frequency and can be used to design hybrid precoders. In this paper, we first proposed a highly mobile hybrid mmWave multi-user (MU) multiple input multiple output (MIMO) system based on transition probabilities which can represent moving action of the MU. Secondly, we investigate compressive sensing based spatial channel covariance estimation based on the proposed dynamic system. We then propose a dynamic covariance forward-backward pursuit (DCFBP) algorithm which introduces forward and backward mechanisms to reconstruct the Hermitian sparse covariance matrix. We further explore the constructed MU sensing matrix quality for conventional sparse Bayesian learning (SBL) framework. The updated sparse Bayesian learning (Updated-SBL) algorithm is developed to reduce the total squared coherence of a constructed sensing matrix with updated receive precoder. Numerical analysis demonstrates the proposed DCFBP method outperforms the benchmark methods. The total squared coherence of the proposed Updated-SBL algorithm is dramatically reduced. and the superiority of this algorithm is validated compared with other benchmark methods with comparable computation complexity.

The availability of the radio spectrum is limited. To compromise the increasing demand for high data rate devices, this fixed spectrum need to be used efficiently. The existing challenge is that the larger portion of the licensed spectrum is underutilized. Cognitive Radio is a technology introduced to help to detect the radio spectrum is occupied or not. Spectrum sensing helps to detect the spectrum holes and provides high spectral resolution capability. This is done using sparse techniques such as Compressive sensing and Sparse Bayesian Learning techniques. Compressive Sensing algorithms such as Basis Pursuit and Orthogonal Matching Pursuit are analyzed. Based on the concept of Sparse Bayesian learning, an expectation maximization algorithm is introduced for spectrum sensing and recovery of the original transmitted signal in cognitive radio systems. Performance comparison is done between proposed algorithms and is validated using Register Transfer Level- Software Defined Radio.

Collaborative Direction of Arrival estimation by using Alternating Direction Method of Multipliers in distributed sensor array networks employing Sparse Bayesian Learning framework

Sparse Bayesian Learning (SBL) is a widely used framework which helps us to deal with two basic problems of machine learning, to avoid overfitting of the model and to incorporate prior knowledge into it. In this work, multiple linear regression models under the SBL framework are used for the problem of multiclass classification when multiple subjects are available. As a case study, we apply our method to the detection of Steady State Visual Evoked Potentials (SSVEP), a problem that arises frequently into the Brain Computer Interface (BCI) paradigm. The multiclass classification problem is decomposed into multiple regression problems. By solving these regression problems, a discriminant vector is learned for further processing. In addition the adoption of the kernel trick and the special treatment of produced similarity matrix provides us with the ability to use a Leave-One-Subject-Out training procedure resulting in a classification system suitable for subject independent classification. Extensive comparisons are carried out between the proposed algorithm, the SVM classifier and the CCA based methodology. The experimental results demonstrate that the proposed algorithm outperforms the competing approaches, in terms of classification accuracy and Information Transfer Rate (ITR), when the number of utilized EEG channels is small.

In image fusion techniques based on joint sparse representation (JSR), the composite image is calculated from the fusion of features, which are represented with sparse coefficients. Orthogonal matching pursuit (OMP) and basis pursuit (BP) are the main candidates to estimate the coefficients. Previously OMP is utilized for the advantage of low complexity. However, noticeable errors occur when the dictionary of JSR cannot ensure the coefficients are sparse enough. Alternatively, BP is more robust than OMP in such cases (though suffered from larger complexity). Unfortunately, it has never been studied in image fusion tasks. In this paper, we investigate JSR based on BP for image fusion. The target is to verify that 1) to what extent can BP outperform OMP; and 2) what is the trade-off between BP and OMP. Finally, we conclude, in some cases, fusion with BP obviously outperforms the one with OMP under an affordable computational complexity.

The impulsive noise and the time-varying channel are two major detrimental factors which greatly constrain the performance of underwater acoustic communications (UACs). Utilizing the joint sparsity of the impulsive noise and the channel impulse response, the paper proposes the generalized approximate message passing (GAMP)-based sparse Bayesian learning (SBL) frameworks for joint impulsive noise mitigation and channel estimation and tracking for orthogonal frequency division multiplexing (OFDM) UACs. Firstly, the SBL framework for the joint estimation is employed. To reduce the computational complexity, the GAMP is introduced into the expectation-maximization (EM) algorithm, and a low-complexity GAMP based SBL framework is formulated without performance degradation. To further estimate and track the impulsive noise and channel state information in the slow time-varying scenarios, we propose a novel GAMP-based temporal SBL framework. The factor graph and GAMP are used to achieve the approximated estimation for the posterior statistics of both the channel state information and the impulsive noise. The algorithm formulates the message passing scheduling for the EM algorithm to solve the joint multiple sparse signal recovery problem. Simulations and sea-trial results demonstrate that the proposed algorithms significantly improve the performance in terms of the mean square error of channel estimation, impulsive noise estimation, bit error rate and computational complexity compared with their corresponding SBL-based counterparts.

Received signal strength (RSS) measurement based source localization is highly dependent on the propagation model. However, such propagation model is not easy to be captured in the practical applications. In this paper, we address the multiple sources localization (MSL) problem while jointly estimating parametric propagation model. Specifically, we model the localization problem as being parameterized by the unknown source locations and propagation parameters. Then, the localization problem is reformulated as a joint parametric sparsifying dictionary learning (PSDL) and sparse signal recovery (SSR) problem. Finally, the problem is solved under the framework of sparse Bayesian learning with parametric dictionary approximation. We compare the proposed method with the state-of-the-art MSL algorithms as well as Cramer-Rao lower bound (CRLB). Numerical simulations highlight the effectiveness of the proposed method.

Steady-state responses (SSRs), evoked by various patterns of periodic stimuli, comprise an important category of evoked potentials. To explore the neural generators of SSRs, a unified framework solving the inverse problem for a single subject or integrating multiple subjects is indispensable. Inspired by the phenomenon that the oscillation frequency of an SSR follows that of the periodic stimulus, we consider the problem of source localization for SSRs using the Fourier components at the stimulation frequency instead of directly using the waveform in this paper. The multi-channel electroencephalogram (EEG) Fourier components at the stimulation frequency is shown to equal multiplying the lead field matrix (LFM) by a complex-valued vector that contains the amplitudes and phases of sources in the cortex, contaminated by spontaneous EEG and electrical noise. This complex-valued inverse problem is further solved in the framework of sparse Bayesian learning, where the non-stationarity of spontaneous EEG among epochs is considered, and the joint sparsity of complex-valued source component vectors is modeled and utilized to improve the source localization performance. Expectation-maximization (EM) is employed to give the ultimate SSR source localization algorithm. By the proposed method, not only a single subject's SSR source localization can be achieved, but also the common locations of a certain type of SSR integrating multiple subjects can be given, even when the electrode layout or number of electrodes varies among subjects. The validity and superior performance of the proposed method was verified by simulations compared with other methods. Real SSR stimulation/recording experiments were also performed, where the electric generators of 40-Hz auditory steady-state responses (ASSRs) by various stimulation patterns were investigated.

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.