Robust Gaussian process regression with G-confluent likelihood

The biased transformation is introduced for continuous random variables. It is proved in this article that the biased transformation works for the generalized Pareto, the generalized extreme value, and the normal distribution. The biased transformation works for important continuous distributions of the exponential family as an approximation; this is demonstrated with the aid of simulations. The new transformation can be used for the Anderson–Darling test for the gamma and beta distribution. The power of the new test procedure is validated by simulations. Finally, a first powerful test is available for the beta distribution although the power function is poor. The χ2-test has lower power. The Kolomogorov–Smirnov test for a fully specified distribution has almost no power in the application for the beta distribution with estimated parameters. The practical relevance of the new test for he beta distribution is demonstrated in an analysis of meteorological data.

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.

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.

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.

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

In this paper, we propose a robust cubature Kalman filter (CKF) for nonlinear state-space models with unknown state and measurement noise covariance matrix. We study situations in which sensors are independent of each other. Therefore, the unknown measurement noise variance is modeled as an unknown inverse gamma (IG) distribution. The Gaussian-Student-t-inverse-Wishart (GSTIW) mixture distribution is used to model the one-step prediction distribution. Modeling generates numerous unknown parameters. Therefore, we adopt the statistical linearization method to linearize the observation function and then estimate the state and parameters separately to reduce the computational burden of estimating unknown parameters, significantly improving the algorithm’s efficiency. Finally, using the variational Bayesian method, a novel and efficient robust CKF based on the IG distribution and GSTIW mixture distributions (IG-GSTIW-CKF) is obtained. Simulation and experimental results show that the proposed method has better estimation accuracy than several advanced algorithms when sensors are independent. In addition, the efficiency of the proposed algorithm is significantly higher than that of other CKF-based methods.

Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations

Wavelet-based demosaicing techniques have the advantage of being computationally relatively fast, while having a reconstruction performance that is similar to state-of-the-art techniques. Because the demosaicing rules are linear, it is fairly simple to integrate denoising into the demosaicing. In this paper, we present a method that performs joint denoising and demosaicing, using a Gaussian Scale Mixture (GSM) prior model, thereby modeling the local edge direction as a hidden variable. The results indicate that this technique offers a better reconstruction performance (in PSNR sense and visually) than sequential demosaicing and denoising. On a recent GPU, our algorithm takes 3.5 s for reconstructing a 12 megapixel RAW digital camera image.

Compressed Sensing (CS) theory has gained so much attention recently in the areas of signal processing. The sparsity of the transform coefficients has been widely employed in the early CS recovery techniques. However, except for the sparsity, there are other priors about transform coefficients such as the tree structure and the statistical dependencies that could be employed in CS reconstruction. In this paper, we propose to introduce the Gaussian Scale Mixtures (GSM) model into the tree structure based Orthogonal Matching Pursuit (TSOMP) reconstruction algorithm. This GSM model can efficiently denote the statistical dependencies between wavelet coefficients. And these statistical dependencies will improve the accuracy of the searching of the tree structure subspace in TSOMP algorithm. When both the inter-scale dependences (such as GSM model) of the coefficients and the intra-scale dependences (such as tree structure) of the coefficients are combined into the Orthogonal Matching Pursuit reconstruction algorithm, the noise and instability in TSOMP reconstruction are well reduced. Some state-of-the-art methods are compared with the proposed method. Experimental results show that the proposed method improves reconstruction accuracy for a given number of measurements and more image details are recovered.

In this article, we examine and provide insights into the frequency domain ICA approach. We develop the concept of a dynamic random process to model the frequency domain source signals. It formalizes the concept of signals that are stationary in a frame but exhibit dynamics at the frame level. Frame dynamics is an important characteristics of these signals and this work demonstrates its significant role in the success of the ICA methods in each frequency bin. We show that the independence between the marginal distributions of the source signals in each frequency bin is related to the independence of the frame dynamics of the time domain source signals. The frame dynamics also naturally leads to the marginal distribution of the source signal in each frequency bin being modeled by a Gaussian scale mixture (GSM). Concentrating on the bin-wise ICA methods, a significant contribution of the paper is to show that signals modeled using variance dependent GSM density can be separated using ICA even though they might be dependent on each other as long as the the frame dynamics of the source signals are different almost surely.

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.

Molecular Communication (MC), a new paradigm of communication, is evolving to serve almost each and every aspect of human life. Noise is one of the serious issue in MC among the fading and interference. Never the less, literatures present various noise models in MC system under different scenarios. Modified Nakagami-m distribution is among the different distribution which is validated experimentally. In this paper, however, we present a new noise distribution namely, Gamma distribution. It is noteworthy to mention that for given set of parameters Gamma distribution represent modified Nakagami-m as it's special case. Moreover, this paper deduces a relation between the PDF of Gamma and Nakagami-m distribution. In addition, derives expression for CDF of Gamma distribution. Finally, PDF of proposed noise distribution is compared with that of Nakagami-m noise distribution.

Variational Bayesian inference based robust multiple measurement sparse signal recovery

We develop a statistical model to describe the spatially varying behavior of local neighborhoods of coefficients in a multiscale image representation. Neighborhoods are modeled as samples of a multivariate Gaussian density that are modulated and rotated according to the values of two hidden random variables, thus allowing the model to adapt to the local amplitude and orientation of the signal. A third hidden variable selects between this oriented process and a nonoriented scale mixture of Gaussians process, thus providing adaptability to the local orientedness of the signal. Based on this model, we develop an optimal Bayesian least squares estimator for denoising images and show through simulations that the resulting method exhibits significant improvement over previously published results obtained with Gaussian scale mixtures.

Gene Networks with Transcriptional Bursting Recapitulate Rare Transient Coordinated High Expression States in Cancer.