Variational Expectation Maximization Method Research Articles

Incorporating grouping information into Bayesian Gaussian graphical model selection

In many applications, we often need to learn the correlation of variables with block structures, and in some challenging genetic data analysis, we even need to learn the overlapping block structures for multiple groups of variables. Incorporating grouping information priors into the learning of Gaussian graphical models in a Bayesian framework is an innovative and feasible approach. We first introduce a Normal-Exponential-Gamma (NEG) structural mixture prior for the elements in the precision matrix. By embedding a structural information prior and a spike-and-slab prior, the Gaussian graphical model can induce two levels of shrinkage: the group level and the individual level. Therefore, a deterministic expectation maximization (EM) method can be used for posterior inference. Second, we add a prior distribution to learn the overlapping block structures. Then, a variational EM method is proposed for posterior inference. Simulation results show that the proposed method is able to estimate the structural sparsity with a smaller estimation bias than the existing alternative methods. Finally we use two sets of data, stock prices and gene expression, to show the application of our method.

Variational EM method for blur estimation using the spike-and-slab image prior

Most state-of-the-art blind image deconvolution methods rely on the Bayesian paradigm to model the deblurring problem and estimate both the blur kernel and latent image. It is customary to model the image in the filter space, where it is supposed to be sparse, and utilize convenient priors to account for this sparsity. In this paper, we propose the use of the spike-and-slab prior together with an efficient variational Expectation Maximization (EM) inference scheme to estimate the blur in the image. The spike-and-slab prior, which constitutes the gold standard in sparse machine learning, selectively shrinks irrelevant variables while mildly regularizing the relevant ones. The proposed variational Expectation Maximization algorithm is more efficient than usual Markov Chain Monte Carlo (MCMC) inference and, also, proves to be more accurate than the standard mean-field variational approximation. Additionally, all the prior model parameters are estimated by the proposed scheme. After blur estimation, a non-blind restoration method is used to obtain the actual estimation of the sharp image. We investigate the behavior of the prior in the experimental section together with a series of experiments with synthetically generated and real blurred images that validate the method's performance in comparison with state-of-the-art blind deconvolution techniques.

Sparse Bayesian Learning Based Three-Dimensional Imaging Algorithm for Off-Grid Air Targets in MIMO Radar Array

In recent years, the development of compressed sensing (CS) and array signal processing provides us with a broader perspective of 3D imaging. The CS-based imaging algorithms have a better performance than traditional methods. In addition, the sparse array can overcome the limitation of aperture size and number of antennas. Since the signal to be reconstructed is sparse for air targets, many CS-based imaging algorithms using a sparse array are proposed. However, most of those algorithms assume that the scatterers are exactly located at the pre-discretized grids, which will not hold in real scene. Aiming at finding an accurate solution to off-grid target imaging, we propose an off-grid 3D imaging method based on improved sparse Bayesian learning (SBL). Besides, the Bayesian Cramér-Rao Bound (BCRB) for off-grid bias estimator is provided. Different from previous algorithms, the proposed algorithm adopts a three-stage hierarchical sparse prior to introduce more degrees of freedom. Then variational expectation maximization method is applied to solve the sparse recovery problem through iteration, during each iteration joint sparsity is used to improve efficiency. Experimental results not only validate that the proposed method outperforms the existing off-grid imaging methods in terms of accuracy and resolution, but have compared the root mean square error with corresponding BCRB, proving effectiveness of the proposed method.