Expectation Propagation for Poisson Data

The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation propagation for approximating the posterior distribution formed from the Poisson likelihood function and a Laplace type prior distribution, e.g., the anisotropic total variation prior. The approach iteratively yields a Gaussian approximation, and at each iteration, it updates the Gaussian approximation to one factor of the posterior distribution by moment matching. We derive explicit update formulas in terms of one-dimensional integrals, and also discuss stable and efficient quadrature rules for evaluating these integrals. The method is showcased on two-dimensional PET images.Comment: 25 pages, to be published at Inverse Problem

Simulated single molecule microscopy with SMeagol

SMeagol is a software tool to simulate highly realistic microscopy data based on spatial systems biology models, in order to facilitate development, validation, and optimization of advanced analysis methods for live cell single molecule microscopy data. Availability and Implementation: SMeagol runs on Matlab R2014 and later, and uses compiled binaries in C for reaction-diffusion simulations. Documentation, source code, and binaries for recent versions of Mac OS, Windows, and Ubuntu Linux can be downloaded from http://smeagol.sourceforge.net.Comment: v2: 14 pages including supplementary text. Pre-copyedited, author-produced version of an application note published in Bioinformatics following peer review. The version of record, and additional supplementary material is available online at: https://academic.oup.com/bioinformatics/article-lookup/doi/10.1093/bioinformatics/btw10

Photometric redshifts and quasar probabilities from a single, data-driven generative model

We describe a technique for simultaneously classifying and estimating the redshift of quasars. It can separate quasars from stars in arbitrary redshift ranges, estimate full posterior distribution functions for the redshift, and naturally incorporate flux uncertainties, missing data, and multi-wavelength photometry. We build models of quasars in flux-redshift space by applying the extreme deconvolution technique to estimate the underlying density. By integrating this density over redshift one can obtain quasar flux-densities in different redshift ranges. This approach allows for efficient, consistent, and fast classification and photometric redshift estimation. This is achieved by combining the speed obtained by choosing simple analytical forms as the basis of our density model with the flexibility of non-parametric models through the use of many simple components with many parameters. We show that this technique is competitive with the best photometric quasar classification techniques---which are limited to fixed, broad redshift ranges and high signal-to-noise ratio data---and with the best photometric redshift techniques when applied to broadband optical data. We demonstrate that the inclusion of UV and NIR data significantly improves photometric quasar--star separation and essentially resolves all of the redshift degeneracies for quasars inherent to the ugriz filter system, even when included data have a low signal-to-noise ratio. For quasars spectroscopically confirmed by the SDSS 84 and 97 percent of the objects with GALEX UV and UKIDSS NIR data have photometric redshifts within 0.1 and 0.3, respectively, of the spectroscopic redshift; this amounts to about a factor of three improvement over ugriz-only photometric redshifts. Our code to calculate quasar probabilities and redshift probability distributions is publicly available

Seeing into Darkness: Scotopic Visual Recognition

Images are formed by counting how many photons traveling from a given set of directions hit an image sensor during a given time interval. When photons are few and far in between, the concept of `image' breaks down and it is best to consider directly the flow of photons. Computer vision in this regime, which we call `scotopic', is radically different from the classical image-based paradigm in that visual computations (classification, control, search) have to take place while the stream of photons is captured and decisions may be taken as soon as enough information is available. The scotopic regime is important for biomedical imaging, security, astronomy and many other fields. Here we develop a framework that allows a machine to classify objects with as few photons as possible, while maintaining the error rate below an acceptable threshold. A dynamic and asymptotically optimal speed-accuracy tradeoff is a key feature of this framework. We propose and study an algorithm to optimize the tradeoff of a convolutional network directly from lowlight images and evaluate on simulated images from standard datasets. Surprisingly, scotopic systems can achieve comparable classification performance as traditional vision systems while using less than 0.1% of the photons in a conventional image. In addition, we demonstrate that our algorithms work even when the illuminance of the environment is unknown and varying. Last, we outline a spiking neural network coupled with photon-counting sensors as a power-efficient hardware realization of scotopic algorithms.Comment: 23 pages, 6 figure

Automated reliability assessment for spectroscopic redshift measurements

We present a new approach to automate the spectroscopic redshift reliability assessment based on machine learning (ML) and characteristics of the redshift probability density function (PDF). We propose to rephrase the spectroscopic redshift estimation into a Bayesian framework, in order to incorporate all sources of information and uncertainties related to the redshift estimation process, and produce a redshift posterior PDF that will be the starting-point for ML algorithms to provide an automated assessment of a redshift reliability. As a use case, public data from the VIMOS VLT Deep Survey is exploited to present and test this new methodology. We first tried to reproduce the existing reliability flags using supervised classification to describe different types of redshift PDFs, but due to the subjective definition of these flags, soon opted for a new homogeneous partitioning of the data into distinct clusters via unsupervised classification. After assessing the accuracy of the new clusters via resubstitution and test predictions, unlabelled data from preliminary mock simulations for the Euclid space mission are projected into this mapping to predict their redshift reliability labels.Comment: Submitted on 02 June 2017 (v1). Revised on 08 September 2017 (v2). Latest version 28 September 2017 (this version v3

4-D Tomographic Inference: Application to SPECT and MR-driven PET

Emission tomographic imaging is framed in the Bayesian and information theoretic framework. The first part of the thesis is inspired by the new possibilities offered by PET-MR systems, formulating models and algorithms for 4-D tomography and for the integration of information from multiple imaging modalities. The second part of the thesis extends the models described in the first part, focusing on the imaging hardware. Three key aspects for the design of new imaging systems are investigated: criteria and efficient algorithms for the optimisation and real-time adaptation of the parameters of the imaging hardware; learning the characteristics of the imaging hardware; exploiting the rich information provided by depthof- interaction (DOI) and energy resolving devices. The document concludes with the description of the NiftyRec software toolkit, developed to enable 4-D multi-modal tomographic inference

Accounting for Calibration Uncertainties in X-ray Analysis: Effective Areas in Spectral Fitting

While considerable advance has been made to account for statistical uncertainties in astronomical analyses, systematic instrumental uncertainties have been generally ignored. This can be crucial to a proper interpretation of analysis results because instrumental calibration uncertainty is a form of systematic uncertainty. Ignoring it can underestimate error bars and introduce bias into the fitted values of model parameters. Accounting for such uncertainties currently requires extensive case-specific simulations if using existing analysis packages. Here we present general statistical methods that incorporate calibration uncertainties into spectral analysis of high-energy data. We first present a method based on multiple imputation that can be applied with any fitting method, but is necessarily approximate. We then describe a more exact Bayesian approach that works in conjunction with a Markov chain Monte Carlo based fitting. We explore methods for improving computational efficiency, and in particular detail a method of summarizing calibration uncertainties with a principal component analysis of samples of plausible calibration files. This method is implemented using recently codified Chandra effective area uncertainties for low-resolution spectral analysis and is verified using both simulated and actual Chandra data. Our procedure for incorporating effective area uncertainty is easily generalized to other types of calibration uncertainties.Comment: 61 pages double spaced, 8 figures, accepted for publication in Ap