Hierarchical Sparse Signal Recovery by Variational Bayesian Inference

Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli–Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

A low-complexity algorithm based on variational Bayesian inference for MIMO channel estimation

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.

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.

Existing studies on sparse Bayesian learning for structural damage detection usually assume that the posterior probability density functions follow standard distributions which facilitate to circumvent the intractable integration problem of the evidence by means of numerical sampling or analytical derivation. Moreover, the uncertainties of each mode are usually quantified as a common parameter to simplify the calculation. These assumptions may not be realistic in practice. This study proposes a sparse Bayesian method for structural damage detection suitable for standard and nonstandard probability distributions. The uncertainty corresponding to each mode is assumed as different. Variational Bayesian inference is developed and the posterior probability density functions of each unknown are individually derived. The parameters are found to follow the gamma distribution, whereas the distribution of the damage index cannot be directly obtained because of the nonlinear relationship in its posterior probability density function. The delayed rejection adaptive Metropolis algorithm is then adopted to generate numerical samples of the damage index. The coupled damage index and parameters in the variational Bayesian inference are successively calculated via an iterative process. A laboratory-tested frame is utilised to verify the effectiveness of the proposed method. The results indicate that the sparse damage can be accurately detected. The proposed method has the advantage of high accuracy and broad applicability.

Robust Bayesian learning approach for massive MIMO channel estimation

Sparse Bayesian learning using correlated hyperparameters for recovery of block sparse signals

We investigate the performance of sparse signal recovery from a set of compressively sensed noisy measurements using variational Bayesian (VB) inference. The framework considered here is sparse Bayesian learning with no specific structure other than sparsity assumed on the signal. Two models are considered here, the issues of each model is studied, and the performances in reconstruction are compared. These models have been already applied to the compressive sensing problems implemented via expectation-maximization algorithm, Markov chain Monte Carlo (MCMC), etc., for different structures of the solution. However, the issues when using variational Bayes inference for only promoting the sparsity have not been investigated. This paper provides details on such modeling and the issues accompanied with each modeling are discussed.

Aiming at DOA estimation under impulsive noise, this paper propose a real-valued sparse Bayesian learning (SBL) method. A unitary transformation is utilized to convert complex-valued direction-of-arrival (DOA) estimation into real ones. The variational Bayesian inference (VBI) technique is then adopted to perform the Bayesian inference with such real-valued prior. Consequently, the computational complexity of this Bayesian inference is significantly reduced. Simulation outcomes demonstrate the great robust performance and low computational load of the new method.

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.

Cloud radio access network (C-RAN) is recognized as a key technology for the fifth generation (5G) wireless communication systems, where machine-type communication (MTC) is considered to support devices' connectivity. In this letter, we study the user activity detection (UAD) and channel estimation (CE) problems in C-RAN for MTC. Based on the user activity sparsity and signal spatial sparsity in C-RAN, we build a two-layer prior distribution graphical model to exploit the sparsity property and analyze the problem with variational Bayesian inference (VBI). We find that the width of prior distribution has a considerable impact on the algorithm performance and propose a modified VBI algorithm. Simulation results are presented to show that the proposed algorithm can achieve better performance with lower complexity than the existing approaches.

Orthogonal time frequency space (OTFS) is a new emerging modulation scheme that performs better than orthogonal frequency division multiplexing (OFDM) in high mobility scenarios. In this paper, we consider the delay-Doppler (DD) channel estimation problem in an OTFS system. By exploiting the inherent sparse nature of the DD channel, the channel estimation problem is modeled as a sparse signal recovery problem. Next, we build a two-layer graphical model with the Laplacian scale mixture (LSM) prior utilized to model the sparse channel. Then, a variational Bayesian inference (VBI) based algorithm is proposed to solve this problem. Simulation results are presented to show that the proposed algorithm can achieve better performance than other existing channel estimation algorithms.

Uncertainty propagation using infinite mixture of Gaussian processes and variational Bayesian inference

Future mobile networks are projected to support integrated sensing and communications in high-speed communication scenarios. Nevertheless, large Doppler shifts induced by time-varying channels may cause severe inter-carrier interference (ICI). Frequency domain shows the potential of reducing ISAC complexity as compared with other domains. However, parameter mismatching issue still exists for such sensing. In this paper, we develop a novel sensing scheme based on sparse Bayesian framework, where the delay and Doppler estimation problem in time-varying channels is formulated as a 3D multiple measurement-sparse signal recovery (MM-SSR) problem. We then propose a novel two-layer variational Bayesian inference (VBI) method to decompose the 3D MM-SSR problem into two layers and estimate the Doppler in the first layer and the delay in the second layer alternatively. Subsequently, as is benefited from newly unveiled signal construction, a simplified two-stage multiple signal classification (MUSIC)-based VBI method is proposed, where the delay and the Doppler are estimated by MUSIC and VBI, respectively. Additionally, the Cramér-Rao bound (CRB) of the considered sensing parameters is derived to characterize the lower bound for the proposed estimators. Corroborated by extensive simulation results, our proposed method can achieve improved mean square error (MSE) than its conventional counterparts and is robust against the target number and target speed, thereby validating its wide applicability and advantages over prior arts.

In this letter, we propose a novel ship detection method in synthetic aperture radar (SAR) imagery via variational Bayesian inference. First, we establish the ship detection probabilistic model which decomposes the SAR image as the sum of a sparse component associated with ships and a sea clutter component. Then, we introduce hierarchical priors of the latent variables in the model and use variational Bayesian inference to estimate the posterior distributions of the latent variables. The proposed method is an automatic iterative process without any sliding window. Experimental results accomplished over synthetic data and a RADARSAT-2 SAR image demonstrate that the proposed method can achieve state-of-the-art ship detection performance.