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

Dynamic light scattering (DLS) is a promising technique for early cataract detection and for studying cataractogenesis. A novel probabilistic analysis tool, the sparse Bayesian learning (SBL) algorithm, is described for reconstructing the most-probable size distribution of α-crystallin and their aggregates in an ocular lens from the DLS data. The performance of the algorithm is evaluated by analyzing simulated correlation data from known distributions and DLS data from the ocular lenses of a fetal calf, a Rhesus monkey, and a man, so as to establish the required efficiency of the SBL algorithm for clinical studies.

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.

Compressive sensing based techniques have recently been applied successfully to underwater acoustics problems such as beamforming and matched field processing. Sparse Bayesian Learning (SBL) is one of the fast compressive sensing methods and is formulated using Bayesian statistics. In the SBL framework, source amplitudes are modeled as complex Gaussian random variables with unknown variance. Evidence maximization is performed to estimate the unknown source amplitude variance and source position. A major advantage of SBL over more commonly used methods such as basis pursuit is that it is computationally faster. In this work, we develop a robust sparse Bayesian learning algorithm that can account for model mismatch leading to errors in the replica vector dictionary. Specifically, the likelihood function is modified so that it takes into account the covariance matrix of error in replica vectors. We also extend the SBL algorithm to process observations from multiple frequencies. The derived update rule combines observations from all the frequencies in a holistic manner. We demonstrate the robust SBL algorithm with simulations. A comparison is done with other compressed sensing methods including basis pursuit and orthogonal matching pursuit.

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.

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.

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.

Space-time adaptive processing (STAP) plays an essential role in clutter suppression and moving target detection in airborne radar systems. The main difficulty is that independent and identically distributed (i.i.d) training samples may not be sufficient to guarantee the performance in the heterogeneous clutter environment. Currently, most sparse recovery/representation (SR) techniques to reduce the requirement of training samples still suffer from high computational complexities. To remedy this problem, a fast group sparse Bayesian learning approach is proposed. Instead of employing all the dictionary atoms, the proposed algorithm identifies the support space of the data and then employs the support space in the sparse Bayesian learning (SBL) algorithm. Moreover, to extend the modified hierarchical model, which can only apply to real-valued signals, the real and imaginary components of the complex-valued signals are treated as two independent real-valued variables. The efficiency of the proposed algorithm is demonstrated both with the simulated and measured data.

Sparse recovery algorithms have been applied to the Space‐time adaptive processing for reducing the requirement of samples over the past 15 years. However, many Sparse recovery algorithms are not robust and need accurate user parameters. Conventional sparse Bayesian learning (SBL) algorithms are insensitivity to user parameters but converge slowly. To remedy the limitation, two iterative reweighted algorithms are proposed based on SBL. In order to minimise the SBL penalty function, we construct its upper‐bounding surrogate function via the concave conjugate function and apply iterative reweighted algorithms to minimise the surrogate function. Theoretical analysis and numerical experiments all exhibit great performance of the proposed algorithms.

In bearing fault diagnosis, identifying fault features under strong background noise is a challenging task. As the weak fault signal of bearing is often interfered by noise, it's easy to cause the signal-noise ratio to be low. We combine the advantages of both variational modal decomposition (VMD) and sparse Bayesian learning (SBL) algorithms and propose a Group-Sparsity Learning Algorithm for Bearing Fault Diagnosis (VMD-SBGSL) based on the VMD and SBL. Compared with the traditional SBL, the proposed framework captures the group-sparsity structure of fault pulses, not only its own accuracy, but also the influence of adjacent accuracy is considered. The method firstly performs variational modal decomposition on the fault signal, selects the optimal modal number K and selects the optimal Intrinsic Mode Function (IMF) according to specific rules. Then use Variational Bayesian Inference (VBI) to solve the optimized SBGSL algorithm to recover the faulty pulse signal. No prior knowledge and no manual tuning of parameters is required in this process. Finally, envelope analysis is performed on the extracted results to identify bearing fault features. The method is applied to the actual fault data of rolling bearings and the comparison with two existing methods was carried out. According to the results, the method can effectively eliminate the interference of noise and can achieve accurate diagnosis of rolling bearing faults.

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).

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

We consider the problem of recovering an image using block compressed sensing (BCS). Traditional BCS algorithms recovers each image block independently and utilizes post-processing methods for removing the blocking artifacts. In contrast, we propose an image recovery method free of post-processing, where we utilize a lapped transform (LT) for the sparse representation of the image in order to reduce the blocking artifacts. Specifically, we derive an iterative image reconstruction method, where a small number of adjacent measurement blocks are jointly processed for recovering an image block. For this purpose, we propose a novel sparse Bayesian learning (SBL) algorithm.

In this study, we developed numerical methods for investigating the sources of epileptic activity from intracranial EEG recordings acquired from intracranial subdural electrodes (iEEG) in patients undergoing pre-surgical evaluation at the epilepsy center of the Mayo Clinic (Rochester, MN). The data were analyzed using independent component analysis (ICA), which identifies and isolates maximally independent signal components in multi-channel recordings. A realistic individual head model was constructed for a patient undergoing pre-surgical evaluation. Structural models of gray matter, white matter, CSF, skull, and scalp were extracted from pre-surgical MR and post-surgical CT images. The electromagnetic source localization forward problem was solved using the Boundary Element Method (BEM). Source localization was performed using the Sparse Bayesian Learning (SBL) algorithm. The multiscale patch-basis source space constructed for this purpose includes a large number of dipole elements on the cortical layer oriented perpendicular to the local cortical surface. These source dipoles are combined into overlapping multi-scalepatches. Using this approach, we were able to detect seizure activity on sulcal walls and on gyrus of the cortex.

We propose a belief propagation (BP) based sparse Bayesian learning (SBL) algorithm, referred to as the BP-SBL, for sparse signal recovery in large scale compressed sensing problems. BP-SBL is based on a widely-used hierarchical Bayesian model. We convert this model to a factor graph and then apply BP to achieve computational efficiency. The computational complexity of BP-SBL is almost linear with respect to the number of transform coefficients, allowing the algorithms to deal with large scale compressed sensing problems efficiently. Numerical examples are provided to demonstrate the effectiveness of BP-SBL.

In this paper, we develop a new sparse Bayesian learning method for recovery of block-sparse signals with un- known cluster patterns. A pattern-coupled hierarchical Gaussian prior model is introduced to characterize the statistical depen- dencies among coefficients, where a set of hyperparameters are employed to control the sparsity of signal coefficients. Unlike the conventional sparse Bayesian learning framework in which each individual hyperparameter is associated independently with each coefficient, in this paper, the prior for each coefficient not only involves its own hyperparameter, but also the hyperparameters of its immediate neighbors. In doing this way, the sparsity patterns of neighboring coefficients are related to each other and the hierarchical model has the potential to encourage structured- sparse solutions. The hyperparameters, along with the sparse signal, are learned by maximizing their posterior probability via an expectation-maximization (EM) algorithm. Index Terms— Sparse Bayesian learning, pattern-coupled hi- erarchical model, block-sparse signal recovery.