Variational Bayesian Compressive Multipolarization Indoor Radar Imaging

This paper proposes a rank-deficient and sparse penalized optimization method for addressing the problem of through-wall radar imaging (TWRI) in the presence of structured wall clutter. Compressive TWRI enables fast data collection and accurate target localization, but faces with the challenges of incomplete data measurements and strong wall clutter. This paper handles these challenges by formulating the task of wall-clutter removal and target image reconstruction as a joint low-rank and sparse regularized minimization problem. In this problem, the low-rank regularization is used to capture the low-dimensional structure of the wall signals and the sparse penalty is employed to represent the image of the indoor targets. We introduce an iterative algorithm based on the forward-backward proximal gradient technique to solve the large-scale optimization problem, which simultaneously removes unwanted wall clutter and reconstruct an image of indoor targets. Simulated and real radar data are used to validate the effectiveness of the proposed rank-deficient and sparse regularized optimization approach.

This dissertation focuses on the development of multiple imputation models and algorithms for high-dimensional data with variable selection structures. Leveraging on the multivariate linear mixed-effects model with missing responses for clustered data, we incorporate the variable selection routines using spike-and-slab priors within the Bayesian variable selection framework. Specific choice of these priors allow us to "force'' variables of importance (e.g. design variables or variables known to play role in missingness mechanism) into the imputation models. Our ultimate goal is to improve computational speed by removing unnecessary variables. Markov chain Monte Carlo techniques have been designed to sample from the implied posterior distributions for model unknowns as well as missing data. A computationally efficient alternative, namely, variational inference algorithms have also been developed to overcome the computational burden of Markov chain Monte Carlo for sampling the posterior predictive distribution missing data. The continuous imputation model and algorithm can be easily modified through a calibration-based rounding strategy for multiple imputation of categorical variables. We also compare two imputation strategies, i.e., the sequential imputation and the joint modeling imputation, has been made in the presence of variable selection structures. We design a joint modeling based imputation framework using a nonparametric Bayesian Dirichlet process mixture model together with a sparse precision matrix model. Two computational algorithms have been carefully designed: the Gibbs sampler and the variational Bayesian inference algorithm. The proposed methodology can be applied to both continuous and mixed continuous and categorical missing data.

A key problem in statistics and machine learning is inferring suitable structure of a model given some observed data. A Bayesian approach to model comparison makes use of the marginal likelihood of each candidate model to form a posterior distribution over models; unfortunately for most models of interest, notably those containing hidden or latent variables, the marginal likelihood is intractable to compute. We present the variational Bayesian (VB) algorithm for directed graphical mod- els, which optimises a lower bound approximation to the marginal likelihood in a procedure similar to the standard EM algorithm. We show that for a large class of models, which we call conjugate exponential, the VB algorithm is a straightfor- ward generalisation of the EM algorithm that incorporates uncertainty over model parameters. In a thorough case study using a small class of bipartite DAGs con- taining hidden variables, we compare the accuracy of the VB approximation to existing asymptotic-data approximations such as the Bayesian Information Crite- rion (BIC) and the Cheeseman-Stutz (CS) criterion, and also to a sampling based gold standard, Annealed Importance Sampling (AIS). We nd that the VB algo- rithm is empirically superior to CS and BIC, and much faster than AIS. Moreover, we prove that a VB approximation can always be constructed in such a way that guarantees it to be more accurate than the CS approximation.

This letter presents a joint impulsive noise mitigation and sparse channel estimation algorithm for single-carrier systems in mobile underwater acoustic communication (UAC) to address the challenges posed by impulsive noise interference. The basis expansion model (BEM) is introduced to describe the underwater acoustic time-varying channels and reduce the channel parameters to be estimated. Based on the model, the variational Bayesian inference algorithm is employed to derive an iterative estimation expression for jointly estimating the sparse BEM channel coefficients and the impulsive noise. The proposed algorithm mitigates the impact of impulsive noise, leading to enhanced communication reliability. Simulations and sea trials validate the effectiveness of the proposed algorithm, highlighting its potential for practical applications in mobile underwater acoustic communication systems.

Estimating depth from a single image is a very challenging and exciting topic in computer vision with implications in several application domains. Recently proposed deep learning approaches achieve outstanding results by tackling it as an image reconstruction task and exploiting geometry constraints (e.g., epipolar geometry) to obtain supervisory signals for training. Inspired by these works and compelling results achieved by Generative Adversarial Network (GAN) on image reconstruction and generation tasks, in this paper we propose to cast unsupervised monocular depth estimation within a GAN paradigm. The generator network learns to infer depth from the reference image to generate a warped target image. At training time, the discriminator network learns to distinguish between fake images generated by the generator and target frames acquired with a stereo rig. To the best of our knowledge, our proposal is the first successful attempt to tackle monocular depth estimation with a GAN paradigm and the extensive evaluation on CityScapes and KITTI datasets confirm that it enables to improve traditional approaches. Additionally, we highlight a major issue with data deployed by a standard evaluation protocol widely used in this field and fix this problem using a more reliable dataset recently made available by the KITTI evaluation benchmark.

Secret shared multiple-image encryption based on row scanning compressive ghost imaging and phase retrieval in the Fresnel domain

Traditional single-pixel imaging systems are aimed mainly at relatively static or slowly changing targets. When there is relative motion between the imaging system and the target, sizable deviations between the measurement values and the real values can occur and result in poor image quality of the reconstructed target. To solve this problem, a novel dynamic compressive imaging system is proposed. In this system, a single-column digital micro-mirror device is used to modulate the target image, and the compressive measurement values are obtained for each column of the image. Based on analysis of the measurement values, a new recovery model of dynamic compressive imaging is given. Differing from traditional reconstruction results, the measurement values of any column of vectors in the target image can be used to reconstruct the vectors of two adjacent columns at the same time. Contingent upon characteristics of the results, a method of image quality enhancement based on an overlapping average algorithm is proposed. Simulation experiments and analysis show that the proposed dynamic compressive imaging can effectively reconstruct the target image; and that when the moving speed of the system changes within a certain range, the system reconstructs a better original image. The system overcomes the impact of dynamically changing speeds, and affords significantly better performance than traditional compressive imaging.

Signal sampling is a bridge to analog source signal and digital signal. Over the years, the base theory of signal sampling is the famous Nyquist sampling theorem, but a large amount of data generated by the waste of storage space. Compressed Sensing proposes a new sampling theory that can sample signals well below the Nyquist sampling rate. Also, the varied reconstruction algorithms of CS can faithfully reconstruct the original signal back from fewer compressive measurements. Therefore, the theory of compressed sensing has been widely used in many fields such as analog-to-signal conversion, synthetic aperture radar imaging, and speech recognition. This paper first elaborates the basic theory model of compressed sensing and focuses on the latest developments in the three aspects of signal sparse transformation, observation matrix design, and reconstruction algorithms. Then this paper also reviews several open problems in CS theory and discusses the existing difficult problems. Secondly, the application and development of compressed sensing in the imaging field are described in detail, compressive imaging technology breaks through the traditional imaging system design concept and uses hardware to achieve non-adaptive linear projection of the target image, thereby achieving the purpose of acquiring a high-precision target image with a smaller number of detectors. And in-depth discussion and analysis of current common compressive imaging systems. Finally, this paper also highlights some of the challenges and research directions in this field.

This paper studies a new Bayesian optimization algorithm for fusing hyperspectral and multispectral images. The hyperspectral image is supposed to be obtained by blurring and subsampling a high spatial and high spectral target image. The multispectral image is modeled as a spectral mixing version of the target image. By introducing appropriate priors for parameters and hyperparameters, the fusion problem is formulated within a Bayesian estimation framework, which is very convenient to model the noise and the target image. The high spatial resolution hyperspectral image is then inferred from its posterior distribution. To compute the Bayesian maximum a posteriori estimator associated with this posterior, an alternating direction method of multipliers within block coordinate descent algorithm is proposed. Simulation results demonstrate the efficiency of the proposed fusion method when compared with several state-of-the-art fusion techniques.

Book-to-market, dividend yield, and expected market returns: A time-series analysis

The Bayesian approach to statistical inference is based on a subjective interpretation of probability. Given a prior distribution describing our prior beliefs concerning the value of an unknown quantity, Bayes' theorem allows us to update those beliefs in the light of observed data. The resulting posterior distribution then summarizes all the available information about the quantity of interest, conditional on the posited model. Bayesian methods for the analysis of categorical data use the same classes of models as the classical approach. However, Bayesian analyses can be more informative – the posterior distribution of the parameter contains more information than mere point estimates or test statistics – and may provide more natural solutions in certain situations such as those involving sparse or missing data, or unidentifiable parameters.

This paper aims at the problems of small Radar Cross-Section (RCS) and short coherent accumulation time in radar detection of low altitude small UAVs. An Inverse Synthetic Aperture Radar (ISAR) super-resolution imaging method based on Bayesian Statistical Machine Learning is proposed. The sparse prior characteristics of UAV with respect to the air-background is utilized by introducing a heavy-tailed Laplacian prior probability distribution, and a Bayesian posterior inference model is derived based on the Gaussian distribution assumption of observation system noise. In view of the non-conjugation of prior distribution, a hierarchical Bayesian model is introduced. Finally, the variational Bayesian expectation maximization algorithm is applied, and the posterior probability density function of the target is solved analytically. Meanwhile, the imaging defocus caused by the non-systematic translational error of the target is corrected, cooperatively. Compared with traditional methods, this method can effectively solve the problem of low imaging signal-to-noise ratio caused by the small RCS of UAV target and low imaging resolution caused by the short coherent accumulation time. The experimental results of simulation and radar data prove the effectiveness and superiority of the proposed method.

Hidden Markov Random Field (HMRF) models are important statistical tools for image segmentation. However, such models cannot automatically determine the number of clusters. In many practical applications, to determine the number of clusters in advance is impossible. The Dirichlet process mixture (DPM) models are nonparametric Bayesian models which can automatically determine the number of clusters for the clustering problem. A new HMRF model which combines the DPM model with Student's t-distribution is proposed in this paper. Compared to the Gaussian distribution, the Student's t-distribution with heavier-tailed can have more applications. This model can automatically determine the appropriate clustering number from the observed data. In addition, an efficient variational Bayesian inference algorithm is derived to the proposed model. Experimental results show that the proposed model outperforms other DPM-based models in image segmentation.

Data-driven techniques such as principal component analysis (PCA) have been widely used to derive predictive models from historical data and applied for quality prediction in industry. Motivated by reducing data collinearity and extracting informative driving forces behind data, latent variable models are explored to facilitate the prediction by regressing data on a set of extracted features. In this paper, a novel learning strategy is proposed to build dynamic features under a full Bayesian framework, incorporating data information and prior knowledge of process dynamics. Unlike the traditional PCA that extracts features based on variances explained, in this paper, the latent features are extracted with the guidance of preferred velocities of nominal variations. By applying Bayesian learning algorithms, parameters are estimated with probability distributions accounting for corresponding uncertainties, and the number of latent features can be automatically determined by the variational Bayesian inference algorithm. The effectiveness and practicability of this Bayesian dynamic feature regression are demonstrated through simulated examples as well as an industrial case study.

Physical layer signal processing algorithms in the wireless domain are seeing increased use of machine learning algorithms, especially Bayesian methods. This work presents the hardware architecture and implementation of a vector processor for one such application, Bayesian channel estimation (CE) (BCE). The BCE vector processor supports a generic instruction set with a supplement of specialized instructions to realize Bayesian algorithms in the signal processing context. The vector processor is designed to work as an accelerator in a system-on-chip (SoC) with an AHB/AXI bus interface or as stand-alone unit. The vector processor achieves more than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times $ </tex-math></inline-formula> improvement in performance when compared with a traditional CE algorithm running on a commercial vector processor. To the best of authors knowledge, this is a first known hardware implementation of a variational Bayesian inference algorithm for a wireless communication application.