Stationary point variational Bayesian attribute-distributed sparse learning with ℓ<inf>1</inf> sparsity constraints

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.

Observations of 1-s average concentration fluctuations during two trials of a U.S. Army diffusion experiment are presented and compared with model predictions based on an exponential probability density function (pdf). The source is near the surface and concentration monitors are on lines about 30 to 100 m downwind of the source. The observed ratio of the standard deviation to the mean of the concentration fluctuations is about 1.3 on the mean plume axis and 4 to 5 on the mean plume edges. Plume intermittency (fraction of non-zero readings) is about 50%; on the mean plume axis and 10%; on the mean plume edges. A meandering plume model is combined with an exponential pdf assumption to produce predictions of the intermittency and the standard deviation of the concentration fluctuations that are within 20%; of the observations.

In this paper, we focus on a multi-task sparse Bayesian learning (SBL) theory that simultaneously utilizes multiple measurement vectors that are marked by a similar sparseness profile. Joint learning for sparse representations of multiple tasks has been mostly overlooked, although it is a useful tool for exploiting data redundancy by modeling the statistical relationships within groups of measurements. We first present a hierarchical Bayesian model and Bayesian inference framework for the multi-task SBL algorithm. Then we investigate the application of the multi-task SBL for model updating in structural health monitoring. The results verify that exploiting common information among multiple related tasks leads to better performance of the Bayesian inversion

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.

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.

Two-dimensional large-eddy simulations of bluff-body stabilized flames of methane and propane, exhibiting significant finite-rate chemistry effects, are presented. A partial equilibrium/two-scalar exponential probability density function (PDF) combustion submodel is applied at the subgrid level. Subgrid scale motions are modelled with a first-order closure employing an anisotropic subgrid eddy-viscosity and two equations for the subgrid turbulent kinetic and scalar energies. Statistical independence of the joint PDF scalars is avoided and the necessary moments are obtained from an extended scale-similarity assumption. Extinction is accounted for by comparing the local turbulent Damköhler number against a ‘critical’ local limit related to the Gibson scalar scale and the reaction zone thickness in mixture fraction space. The post-extinction regime is modelled via a Lagrangian transport equation for a reactedness progress variable which follows a linear deterministic relaxation to its mean value (interaction by exchange with the mean model; IEM).Comparisons between simulations and measurements suggested the ability of the adopted methodology to represent the experimental variations in the momentum and scalar fields at conditions close to the lean or the rich blow-out limit. Favourable agreement was achieved in the calculation of the recirculation lengths and the peak temperature and turbulence levels in the near-wake region. Significant experimental trends, such as the suppression of the large-scale organized motions in the developing wake at low and medium fuel injection rates, and the re-emergence of the quasi-periodic shedding activity close to the lean limit, were also reproduced. Quantitative discrepancies increased in the prediction of major species, but the measured trends due to the effects of partial extinction were adequately recovered.

The performance of various discrete adaptive delta modulation (ADM) systems in the presence of random signal input is analyzed. The ADM systems considered are (a) Winkler system, (b) Abate (1967) system, (c) Bosworth and Candy (1968) system, and (d) Tazaki system (1977). It is assumed that the input random signal has a slope which varies randomly having Gaussian, Rayleigh and exponential probability density function (PDF) and has rectangular and triangular power spectral density (PSD). For an input random signal with specific PSD and PDF of its slope, the SNR has been calculated and plotted against the signal power. A performance evaluation has been made and summarized for the four systems above. >

This study aims to assess the marine hydrodynamics and the potential power of sea currents by simulating the probability distribution functions of the sea current velocity values. For this aim, hourly sea current velocity and direction data measured from the Çanakkale (Turkey) measurement station in the North Aegean Sea were used. These data were measured during two separate periods: January 1 – March 24, 2017, and March 25 – December 31, 2019. First, the vertical structure of the sea currents up to 50 m depth was determined. Then, frequency distributions of hourly sea current velocities were modeled by using the Weibull, Rayleigh, and Exponential probability density functions. According to the results obtained at 5, 10, 20, 30, 40, and 50 m depths below the sea surface level, the annual sea current velocity was 28.8 ± 0.395, 26.1 ± 0.388, 19.4 ± 0.339, 16.1 ± 0.324, 17.5 ± 0.344, and 24.7 ± 0.622 cm/s, respectively, in this sea. Furthermore, the annual sea current power potential was calculated as 30.0, 25.4, 15.0, 12.2, 15.0, and 88.2 W/m2 for 5, 10, 20, 30, 40, and 50 m depths, respectively. The results demonstrated that the Weibull distribution model was the best fit for the sea current velocity in this sea.

Software maintenance phase involves modifying and making changes to software due to requirements changes and/or defects reported by users. At this phase, when defects are uncovered, users will inform the problem to software maintenance team. The team has to provide the users the estimated fixing time and then fix the errors. Fault reparation/fixing time of different kinds of errors may be varied due to fault types and program complexity. In this research, an approach to estimate fault reparation time is proposed. The exponential probability density function is mainly used to construct the estimation model. An evaluation of the approach is present by applying the approach to open source software projects. A comparison of fault reparation time estimation between considering fault types and without fault types is reported.

The paper deals with assessing blur amount in images. Blur is a common artefact that attenuates the high frequency components of an image. The main idea turns on analysing the frequency response at transitions through resolutions. To achieve that, the histogram of the multiresolution DCT coefficients is modelled by using an exponential probability density function (pdf). The steepness of the pdf is used as a cue to characterize the blur effect. Faithful scores are obtained while testing the proposed approach on five image collections. The proposed measure is validated on the JPEG2000 lossy compression algorithm and the Lucy-Richardson iterative deblurring approach.

A method for modeling the effects of finite-rate chemistry such as partial extinctions and reignitions is developed and used to compute turbulent CO/H2/N2 or CH4-air-piloted jet diffusion flames close to extinction. The method is combined with a two-dimensional Large Eddy Simulation procedure employing a partial equilibrium/two-scalar exponential Probability Density Function (PDF) combustion submodel applied at the subgrid scale (SGS) level. Subgrid motions are modeled with a first-order closure utilizing an anisotropic subgrid eddy-viscosity and two equations for the subgrid scale turbulent kinetic and scalar energies. Statistical independence of the joint PDF scalars is here avoided and the required moments are obtained from an extended scale-similarity assumption. Extinction is determined by comparing the local Damkohler number against a ‘critical’ local limit related to the Gibson scalar scale and the reaction zone thickness. The post-extinction regime is treated with a reactedness progress variable computed from a Lagrangian transport equation and a two-scalar reacledness-mixture fraction presumed PDF. Comparisons with well documented turbulent flame data suggested the ability of the presented methodology to describe many experimental trends and variations of the momentum and reactive scalar mixing fields at flame conditions close to extinction.

In this paper the mean time to acquire a stationary target by n stationary imaging sensors is computed using probability theory by making use of the well established result that the detection time for a single imaging sensor is a random variable from an exponential probability density function. Each imaging sensor is characterized by a separate P∞ value which describes the probability an observer using that sensor will eventually acquire the target and a separate t value which describes the mean time to acquire the target using that sensor. There is no restriction on the wavelength band used by the imaging sensor. There are no empirical constants in the model presented here and the results are in agreement with and generalize previously published equations. The newly developed equations have been verified by numerical simulations and also yield the expected mean detection time for all limiting values of the input parameters. The code used in the numerical simulations is exhibited. For any given scenario, the separate τ observer-sensor-target parameters P∞ and t can be estimated using the NV-IPM model or measured in perception experiments. Thus the input parameters needed by the model are generally available. Comparing results presented here with results from war game simulations such as OneSAF may improve the quality of both products.

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

We present a fully decentralized algorithm that is inspired by sparse Bayesian learning (SBL) and can be used for non-parametric sparse estimation of unknown spatial functions - spatial fields - with wireless sensor networks (WSNs). It is assumed that a spatial field is represented as a linear combination of weighted fixed basis functions. By exploiting the similarity between the topology of a WSN and the proposed probabilistic graphical model for distributed SBL, a combination of variational inference and loopy belief propagation (LBP) is used to obtain the weights and the sparse subset of relevant basis functions. The algorithm requires only transmission between neighboring sensors and no multi-hop communication is needed. Furthermore, it does not rely on a fixed network structure and no information about the total number of sensors in the network is necessary. Due to consensus in the weight parameters between neighboring sensors, it is demonstrated that also the sparsity patterns of relevant basis functions generally agree. The effectiveness of the proposed algorithm is demonstrated with synthetic data.

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.