Image Modelling to Generate a Probabilistic Astronomical Catalogue

20 May 2013

Kilian Walsh

with Prof. David Hogg and Dr. Dustin Lang (CMU)

Goals

  • Astrometry.net
    • Work with the A.n code and data to improve and extend functionality
    • Improved code then allows us to do...
  • Science
    • Build a statistical model of the sky
    • Use this model to make discoveries

How Astrometry.net works

  • Compares sources found in image to a catalogue with "geometric hashing"
    • Super fast and ZERO false positives
  • Can be used to astrometrically calibrate any astronomical image (optical)

Why Astrometry.net?

  • Crowdsource = Lots of data
    • currently 36,323 items on flickr
  • Potential HUGE database (i.e. every image ever) of uniform information, regardless of image source or format

But...

  • Calibration only achieves accurate positions of astronomical sources
  • We would also like to know about source brightnesses - enables more scientific goals
  • Calibration done using an imperfect catalogue (USNO-B)

Introducing the Tractor!

  • Generates "probabilistically justified astronomical catalogues"
    • \( p(\Theta | \{ y_{i} \}) = \frac{p(\{ y_{i} \} | \Theta , I) p(\Theta | I)}{p(\{ y_{i} \} | I)} \) Wahey!
  • Constructs a generative model of the image using Bayesian optimisation by "freezing" and "thawing" parameters

The Plan

  • Feed calibration data from A.n plus some other guesses into the Tractor as "prior" information and construct a likelihood function
    • Likelihood includes noise model (i.e. sky background), source locations, psf, galaxy models
  • 1, 2, ..., Infinity!
  • Eventually... collate parameters from many images and construct metamodel of the sky

Progress

  • Image No. 1 being modelled, many kinks to iron out yet!
    • Some success with fitting galaxy models but optimal ordering of freezing and thawing still troublesome
  • Offshoot project:
    • Find variation in location of sources as compared with catalogue
    • Find "covisibility" of stars across images to improve catalogue

Image 1


Series of Image Synthesis examples with the tractor:

A.n locations added, brightnesses optimised with psf guess


Galaxy selection and psf varied


More conservative galaxy selection


Source shift detection

  • Model individual patches of image containing a single star
  • Model chooses whether star exists in patch, is in catalogue position, or has moved using Bayesian Information Criterion
  • \( BIC = \chi ^{2} + ln(N) K \) for \( K \) the number of parameters
  • Models have sky background (with tilt), psf of circular gaussian, and location of psf centre. Each part is frozen and thawed for each fit, as for tractor.



Thanks!