Camera shake during exposure leads to objectionable image blur and ruins many photographs. Conventional blind deconvolution methods typically assume frequency-domain constraints on images, or overly simplified parametric forms for the motion path during camera shake. Real camera motions can follow convoluted paths, and a spatial domain prior can better maintain visually salient image characteristics. We introduce a method to remove the effects of camera shake from seriously blurred images. The method assumes a uniform camera blur over the image and negligible in-plane camera rotation. In order to estimate the blur from the camera shake, the user must specify an image region without saturation effects. We show results for a variety of digital photographs taken from personal photo collections.

We apply a variational method to automatically determine the number of mixtures of independent components in high-dimensional datasets, in which the sources may be nonsymmetrically distributed. The data are modeled by clusters where each cluster is described as a linear mixture of independent factors. The variational Bayesian method yields an accurate density model for the observed data without overfitting problems. This allows the dimensionality of the data to be identified for each cluster. The new method was successfully applied to a difficult real-world medical dataset for diagnosing glaucoma.

In this paper, we propose novel algorithms for total variation (TV) based image restoration and parameter estimation utilizing variational distribution approximations. Within the hierarchical Bayesian formulation, the reconstructed image and the unknown hyperparameters for the image prior and the noise are simultaneously estimated. The proposed algorithms provide approximations to the posterior distributions of the latent variables using variational methods. We show that some of the current approaches to TV-based image restoration are special cases of our framework. Experimental results show that the proposed approaches provide competitive performance without any assumptions about unknown hyperparameters and clearly outperform existing methods when additional information is included.

Motivation: A number of algorithms and analytical models have been employed to reduce the multidimensional complexity of DNA array data and attempt to extract some meaningful interpretation of the results. These include clustering, principal components analysis, self-organizing maps, and support vector machine analysis. Each method assumes an implicit model for the data, many of which separate genes into distinct clusters defined by similar expression profiles in the samples tested. A point of concern is that many genes may be involved in a number of distinct behaviours, and should therefore be modelled to fit into as many separate clusters as detected in the multidimensional gene expression space. The analysis of gene expression data using a decomposition model that is independent of the observer involved would be highly beneficial to improve standard and reproducible classification of clinical and research samples. Results: We present a variational independent component analysis (ICA) method for reducing high dimensional DNA array data to a smaller set of latent variables, each associated with a gene signature. We present the results of applying the method to data from an ovarian cancer study, revealing a number of tissue type-specific and tissue type-independent gene signatures present in varying amounts among the samples surveyed. The observer independent results of such molecular analysis of biological samples could help identify patients who would benefit from different treatment strategies. We further explore the application of the model to similar highthroughput studies. Availability: Supporting details of the decomposition model can be found at

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Abstract—Following the hierarchical Bayesian framework for blind deconvolution problems, in this paper, we propose the use of simultaneous autoregressions as prior distributions for both the image and blur, and gamma distributions for the unknown parameters (hyperparameters) of the priors and the image formation noise. We show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations. We apply variational methods to approximate the posterior probability of the unknown image, blur, and hyperparameters and propose two different approximations of the posterior distribution. One of these approximations coincides with a classical blind deconvolution method. The proposed algorithms are tested experimentally and compared with existing blind deconvolution methods. Index Terms—Bayesian framework, blind deconvolution, parameter estimation, variational methods. I.

this article, we extend the variational Bayesian ICA method to problemswith missing data. More important, the probability density estimate of the missing entries can be used to #ll in the missing values. This allows the density model to be re#ned and made more accurate

Abstract — Linear factor models with nonnegativity constraints have received a great deal of interest in a number of problem domains. In existing approaches, positivity has often been associated with sparsity. In this paper we argue that sparsity of the factors is not always a desirable option, but certainly a technical limitation of the currently existing solutions. We then reformulate the problem in order to relax the sparsity constraint while retaining positivity. A variational inference procedure is derived and this is contrasted to existing related approaches. Both i.i.d. and first-order AR variants of the proposed model are provided and these are experimentally demonstrated in a real-world astrophysical application. I.

We develop a new component analysis framework, the Noisy-Or Component Analyzer (NOCA), that targets high-dimensional binary data. NOCA is a probabilistic latent variable model that assumes the expression of observed high-dimensional binary data is driven by a small number of hidden binary sources combined via noisy-or units. The component analysis procedure is equivalent to learning of NOCA parameters. Since the classical EM formulation of the NOCA learning problem is intractable, we develop its variational approximation. We test the NOCA framework on two problems: (1) a synthetic image-decomposition problem and (2) a co-citation data analysis problem for thousands of CiteSeer documents. We demonstrate good performance of the new model on both problems. In addition, we contrast the model to two mixture-based latent-factor models: the probabilistic latent semantic analysis (PLSA) and latent Dirichlet allocation (LDA).

This note describes the assumptions underlying the latent-variable-modelling work of Miskin, Martoglio and MacKay for microarrays. The aim is to give a non-technical summary of the model assumptions and the computational methods. For further information, the thesis of James Miskin (2001) should be consulted.