Detecting Unspecified Structure in Low-Count Images

• Activity Number: 335
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): David A. van Dyk* and Nathan Stein and Vinay L. Kashyap and Aneta Siemiginowska
• Companies: Imperial College London and University of Pennsylvania and Smithsonian Astrophysical Observatory and Smithsonian Astrophysical Observatory
• Keywords: Image Analysis ; Astrostatitsics ; Hypothesis testing ; Markov inequality

Abstract

Unexpected structure in images of astronomical sources often presents itself upon visual inspection of the image. Researchers would like a formal statistical test of whether such structure corresponds to actual features in the source or can be attributed to noise in the data. To avoid a biased test, the test must be neutral regarding what constitutes structure; tailoring the alternative hypothesis to a particular feature in the data results in a false detection rate greater than the significance level. We present a neutral test of this sort for pixelated images with Poisson noise. To infer image structure, we conduct a Bayesian analysis of a full model that uses a multi-scale component to allow flexible departures from the posited null model. As a test statistic, we use a tail probability of the posterior distribution under the full model. One novel aspect of our approach is that to reduce the computational demands of simulating under the null, we estimate an upper bound on a p-value, enabled by our choice of test statistic. We demonstrate our method on simulated images and on an X-ray image of a quasar with a possible jet.