Sparse acoustical holography from iterated Bayesian focusing

Image deconvolution is formulated in the wavelet domain under the Bayesian framework. The well-known sparsity of the wavelet coefficients of real-world images is modeled by heavy-tailed priors belonging to the Gaussian scale mixture (GSM) class; i.e., priors given by a linear (finite of infinite) combination of Gaussian densities. This class includes, among others, the generalized Gaussian, the Jeffreys, and the Gaussian mixture priors. Necessary and sufficient conditions are stated under which the prior induced by a thresholding/shrinking denoising rule is a GSM. This result is then used to show that the prior induced by the "nonnegative garrote" thresholding/shrinking rule, herein termed the garrote prior, is a GSM. To compute the maximum a posteriori estimate, we propose a new generalized expectation maximization (GEM) algorithm, where the missing variables are the scale factors of the GSM densities. The maximization step of the underlying expectation maximization algorithm is replaced with a linear stationary second-order iterative method. The result is a GEM algorithm of O(N log N) computational complexity. In a series of benchmark tests, the proposed approach outperforms or performs similarly to state-of-the art methods, demanding comparable (in some cases, much less) computational complexity.

Image restoration (deconvolution) is a basic step for image processing, analysis and computer vision. We addressed blurred image deconvolution problem using Expectation maximization (EM) based approach in the wavelet domain. The sparsity property of wavelet coefficients is modelled using the class of Gaussian Scale Mixture (GSM), which represents the heavy-tailed statistical distribution. The maximum a posterior (MAP) estimate is computed using EM, where scale factors of GSM plays the role of hidden variables. The estimated hidden scaling variables are then used to restore the original image. Although similar formulations have been proposed before but the resulting optimization problems have been computationally demanding and sometimes depends heavily on the initial values of parameters. We proposed an optimized Bayesian approach in wavelet domain to restore an image degraded by linear distortion (e.g., blur) and additive Gaussian noise. Simulation results are presented to demonstrate the quality of our method, over a wide range of blur and noise level, both visually and in terms of signal to noise ratio.

Attack to security of watermarking is to estimate secret keys used in watermarking communications. The security level of watermarking algorithms can be evaluated by Cramer-Rao Bound (CRB) for the estimation of secret keys. As a widely used method, Add-Spread-Spectrum (Add-SS) watermarking has drawn a lot of attention. Previous work on watermarking security is mainly based on the assumption that the host is Gaussian distributed and ignores the impact of the non-Gaussian characteristics of natural images. With the incorporation of Gaussian Scale Mixture (GSM) model for host signals, this paper presents a theoretical analysis on the security of the Add-SS watermarking algorithms. By giving the CRB and Modified Cramer-Rao Bound (MCRB) for the estimation of secret carriers under Known Message Attack (KMA) and Watermarked Only Attack (WOA), this paper also reveals the factors that may influence the security of Add-SS based watermarking algorithms. Results presented in this paper are very helpful for designing the new generation of secure and robust watermarking system.

A new crack identification method that estimates the cracks in invisible locations based on the surface deformation measured by digital image correlation (DIC) is developed. An inverse problem is setup to estimate such invisible cracks from surface deformations. The inverse problem has an ill-condition because of noise contained in surface deformations. Our proposed regularization method uses prior information and Expectation a Posteriori (EAP) estimation. Prior information includes candidate crack shapes and surface deformations due to cracks. The candidate crack shapes are created by determining a crack's starting point and propagating it based on the force at its perimeter (ligament). A prior distribution is the surface deformations due to the candidate crack shapes. The likelihood distribution is a surface deformation measured by the DIC method. A posterior distribution is defined from the prior and likelihood distributions. In this study, the estimated result is the expected value of the posterior distribution. The validation test was performed, and the result shows that the proposed method superior to the conventional L1-norm regularization method.

In Recent days Semi supervised image segmentation techniques play a noteworthy role in image processing. Semi supervised image segmentation needs both labeled data and unlabeled data. It means that a Small amount of human assistance or Prior information is given during clustering process. This paper discusses an enhanced semi supervised image segmentation method from labeled image. It uses both a background selection marker and fore ground object selection marker separately. The EM (Expectation Maximization) algorithm is used for clustering along with must link constraints. The proposed method is applied for natural images using MATLAB 7. Thus the proposed method extracts Object of Interest (OOI) from OONI (Object of Not Interest) efficiently and the experimental results are compared with Standard K Means and EM Algorithm also. The results show that the proposed system gives better results than the other two methods. It may also be suitable for object extraction from natural images and medical image analysis.

This paper considers a hierarchical Bayesian analysis of regression models using a class of Gaussian scale mixtures. This class provides a robust alternative to the common use of the Gaussian distribution as a prior distribution in particular for estimating the regression function subject to uncertainty about the constraint. For this purpose, we use a family of rectangular screened multivariate scale mixtures of Gaussian distribution as a prior for the regression function, which is flexible enough to reflect the degrees of uncertainty about the functional constraint. Specifically, we propose a hierarchical Bayesian regression model for the constrained regression function with uncertainty on the basis of three stages of a prior hierarchy with Gaussian scale mixtures, referred to as a hierarchical screened scale mixture of Gaussian regression models (HSMGRM). We describe distributional properties of HSMGRM and an efficient Markov chain Monte Carlo algorithm for posterior inference, and apply the proposed model to real applications with constrained regression models subject to uncertainty.

We describe an efficient generalized expectation maximization algorithm for estimating the spectral features of a noise source corrupting an observed image. We use a statistical model for images decomposed in an overcomplete oriented pyramid. Each neighborhood of clean pyramid coefficients is modeled as a Gaussian scale mixture, whereas the noise is assumed Gaussian. Combining this GEM technique with a previous Bayesian denoise estimator, we obtain a full blind denoising algorithm, able to deal with homogeneous, Gaussian or mesokurtotic, noise sources of arbitrary covariance. Results demonstrate the high performance of the method for a wide range of corruption sources.

For eukaryotic cells, the biological processes involving regulatory DNA elements play an important role in cell cycle. Understanding 3D spatial arrangements of chromosomes and revealing long-range chromatin interactions are critical to decipher these biological processes. In recent years, chromosome conformation capture (3C) related techniques have been developed to measure the interaction frequencies between long-range genome loci, which have provided a great opportunity to decode the 3D organization of the genome. In this paper, we develop a new Bayesian framework to derive the 3D architecture of a chromosome from 3C-based data. By modeling each chromosome as a polymer chain, we define the conformational energy based on our current knowledge on polymer physics and use it as prior information in the Bayesian framework. We also propose an expectation-maximization (EM) based algorithm to estimate the unknown parameters of the Bayesian model and infer an ensemble of chromatin structures based on interaction frequency data. We have validated our Bayesian inference approach through cross-validation and verified the computed chromatin conformations using the geometric constraints derived from fluorescence in situ hybridization (FISH) experiments. We have further confirmed the inferred chromatin structures using the known genetic interactions derived from other studies in the literature. Our test results have indicated that our Bayesian framework can compute an accurate ensemble of 3D chromatin conformations that best interpret the distance constraints derived from 3C-based data and also agree with other sources of geometric constraints derived from experimental evidence in the previous studies. The source code of our approach can be found in https://github.com/wangsy11/InfMod3DGen.

Neural networks have long been applied to inverse parameter retrieval problems. The literature documents a development from the use of neural networks as explicit inverses to neural network iterative inversion (NNII) and, finally, to Bayesian neural network iterative inversion (BNNII), which adds a Bayesian superstructure to NNII. Inverse problems have been often considered ill posed, i.e. the statement of the problem does not thoroughly constrain the solution space. BNNII takes advantage of this lack of information by adding additional informative constraints to the problem solution using Bayesian methodology. This paper extends BNNII, showing how ground truth information, information regarding the particular parameter contour under reconstruction, and information regarding the underlying physical process, can be seamlessly added to the problem solution. Remote sensing problems afford opportunities for inclusion of ground truth information, prior probabilities, noise distributions, and other informative constraints within a Bayesian probabilistic framework. We apply these Bayesian methods to a synthetic remote sensing problem, showing that the addition of ground truth information, which is naturally included through Bayesian modeling, provides a significant performance improvement.

Occupational exposure assessment is important in preventing occupational coal worker’s diseases. Methods have been proposed to assess compliance with exposure limits which aim to protect workers from developing diseases. A Bayesian framework with informative prior distribution obtained from historical or expert judgements has been highly recommended for compliance testing. The compliance testing is assessed against the occupational exposure limits (OEL) and categorization of the exposure, ranging from very highly controlled to very poorly controlled exposure groups. This study used a Bayesian framework from historical and expert elicitation data to compare the posterior probabilities of the 95th percentile (P95) of the coal dust exposures to improve compliance assessment and decision-making. A total of 10 job titles were included in this study. Bayesian framework with Markov chain Monte Carlo (MCMC) simulation was used to draw a full posterior probability of finding a job title to an exposure category. A modified IDEA (“Investigate”, “Discuss”, “Estimate”, and “Aggregate”) technique was used to conduct expert elicitation. The experts were asked to give their subjective probabilities of finding coal dust exposure of a job title in each of the exposure categories. Sensitivity analysis was done for parameter space to check for misclassification of exposures. There were more than 98% probabilities of the P95 exposure being found in the poorly controlled exposure group when using expert judgments. Historical data and non-informative prior tend to show a lower probability of finding the P95 in higher exposure categories in some titles unlike expert judgments. Expert judgements tend to show some similarity in findings with historical data. We recommend the use of expert judgements in occupational risk assessment as prior information before a decision is made on current exposure when historical data are unavailable or scarce.

This article focuses on data analyses under the scenario of missing at random within discrete-time Markov chain models. The naive method, nonlinear (NL) method, and Expectation-Maximization (EM) algorithm are discussed. We extend the NL method into a Bayesian framework, using an adjusted rejection algorithm to sample the posterior distribution, and estimating the transition probabilities with a Monte Carlo algorithm. We compare the Bayesian nonlinear (BNL) method with the naive method and the EM algorithm with various missing rates, and comprehensively evaluate estimators in terms of biases, variances, mean square errors, and coverage probabilities (CPs). Our simulation results show that the EM algorithm usually offers smallest variances but with poorest CP, while the BNL method has smaller variances and better/similar CP as compared to the naive method. When the missing rate is low (about 9%, MAR), the three methods are comparable. Whereas when the missing rate is high (about 25%, MAR), overall, the BNL method performs slightly but consistently better than the naive method regarding variances and CP. Data from a longitudinal study of stress level among caregivers of individuals with Alzheimer’s disease is used to illustrate these methods.

A strategy is presented to incorporate prior information from conceptual geological models in probabilistic inversion of geophysical data. The conceptual geological models are represented by multiple-point statistics training images (TIs) featuring the expected lithological units and structural patterns. Information from an ensemble of TI realizations is used in two different ways. First, dominant modes are identified by analysis of the frequency content in the realizations, which drastically reduces the model parameter space in the frequency-amplitude domain. Second, the distributions of global, summary metrics (e.g. model roughness) are used to formulate a prior probability density function. The inverse problem is formulated in a Bayesian framework and the posterior pdf is sampled using Markov chain Monte Carlo simulation. The usefulness and applicability of this method is demonstrated on two case studies in which synthetic crosshole ground-penetrating radar traveltime data are inverted to recover 2-D porosity fields. The use of prior information from TIs significantly enhances the reliability of the posterior models by removing inversion artefacts and improving individual parameter estimates. The proposed methodology reduces the ambiguity inherent in the inversion of high-dimensional parameter spaces, accommodates a wide range of summary statistics and geophysical forward problems.

Cerenkov luminescence tomography (CLT) is a promising non-invasive optical imaging method with three-dimensional semiquantitative in vivo imaging capability. However, CLT itself relies on Cerenkov radiation, a low-intensity radiation, making CLT reconstruction more challenging than other imaging modalities. In order to solve the ill-posed inverse problem of CLT imaging, some numerical optimization or regularization methods need to be applied. However, in commonly used methods for solving inverse problems, parameter selection significantly influences the results. Therefore, this paper proposed a probabilistic energy distribution density region scaling (P-EDDRS) framework. In this framework, multiple reconstruction iterations are performed, and the Cerenkov source distribution of each reconstruction is treated as random variables. According to the spatial energy distribution density, the new region of interest (ROI) is solved. The size of the region required for the next operation was determined dynamically by combining the intensity characteristics. In addition, each reconstruction source distribution is given a probability weight value, and the prior probability in the subsequent reconstruction is refreshed. Last, all the reconstruction source distributions are weighted with the corresponding probability weights to get the final Cerenkov source distribution. To evaluate the performance of the P-EDDRS framework in CLT, this article performed numerical simulation, in vivo pseudotumor model mouse experiment, and breast cancer mouse experiment. Experimental results show that this reconstruction framework has better positioning accuracy and shape recovery ability and can optimize the reconstruction effect of multiple algorithms on CLT.

In multi-slice magnetic resonance imaging (MRI), the resolution in the slice direction is usually reduced to allow faster acquisition times and to reduce the amount of noise in each 2D slice. To address this issue, a number of super resolution (SR) methods have been proposed to improve the resolution of 3D MRI volumes. Most of the methods involve the use of prior models of the MRI data as regularization terms in an ill-conditioned inverse problem. The use of user-defined parameters produces better results for these approaches but an inappropriate choice may reduce the overall performance of the algorithm. In this paper, we present a wavelet domain SR method which uses a Gaussian scale mixture (GSM) model in a sparseness constraint to regularize the ill-posed SR inverse problem. The proposed approach also makes use of an extension of the Dual Tree Complex Wavelet Transform to provide the ability to analyze the wavelet coefficients with sub-level precision. Our results show that the 3D MRI volumes reconstructed using this approach have quality superior to volumes produced by the best previously proposed approaches.

This paper introduces an expectation-maximization (EM) algorithm within a wavelet domain Bayesian framework for semi-blind channel estimation of multiband OFDM based UWB communications. A prior distribution is chosen for the wavelet coefficients of the unknown channel impulse response, in order to capture the well known sparseness property of the wavelet representation. This prior yields, in maximum a posteriori estimation, a thresholding rule within the EM algorithm. We particularly focus on reducing the number of estimated parameters by iteratively discarding "unsignificant" wavelet coefficients from the estimation process. In addition, the proposed algorithm enhances the estimation accuracy in terms of mean square error with less computational complexity than traditional semi-blind methods. Simulation results using IEEE UWB channel models show that the proposed algorithm outperforms pilot based channel estimation in terms of mean square error and bit error rate