Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps

We propose to model the image differentials of astrophysical source maps by Student's t-distribution and to use them in the Bayesian source separation method as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC) sampling scheme to unmix the astrophysical sources and describe the derivation details. In this scheme, we use the Langevin stochastic equation for transitions, which enables parallel drawing of random samples from the posterior, and reduces the computation time significantly (by two orders of magnitude). In addition, Student's t-distribution parameters are updated throughout the iterations. The results on astrophysical source separation are assessed with two performance criteria defined in the pixel and the frequency domains.Comment: 12 pages, 6 figure

A stochastic algorithm for probabilistic independent component analysis

The decomposition of a sample of images on a relevant subspace is a recurrent problem in many different fields from Computer Vision to medical image analysis. We propose in this paper a new learning principle and implementation of the generative decomposition model generally known as noisy ICA (for independent component analysis) based on the SAEM algorithm, which is a versatile stochastic approximation of the standard EM algorithm. We demonstrate the applicability of the method on a large range of decomposition models and illustrate the developments with experimental results on various data sets.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS499 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Unifying review of linear gaussian models

Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities, we show how independent component analysis is also a variation of the same basic generative model.We show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models

Toward single particle reconstruction without particle picking: Breaking the detection limit

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. In a cryo-EM experiment, the microscope produces images called micrographs. Projections of the molecule of interest are embedded in the micrographs at unknown locations, and under unknown viewing directions. Standard imaging techniques first locate these projections (detection) and then reconstruct the 3-D structure from them. Unfortunately, high noise levels hinder detection. When reliable detection is rendered impossible, the standard techniques fail. This is a problem especially for small molecules, which can be particularly hard to detect. In this paper, we propose a radically different approach: we contend that the structure could, in principle, be reconstructed directly from the micrographs, without intermediate detection. As a result, even small molecules should be within reach for cryo-EM. To support this claim, we setup a simplified mathematical model and demonstrate how our autocorrelation analysis technique allows to go directly from the micrographs to the sought signals. This involves only one pass over the micrographs, which is desirable for large experiments. We show numerical results and discuss challenges that lay ahead to turn this proof-of-concept into a competitive alternative to state-of-the-art algorithms