Volume 574, February 2015
|Number of page(s)||20|
|Section||Numerical methods and codes|
|Published online||29 January 2015|
Denoising, deconvolving, and decomposing photon observations⋆
Derivation of the D3PO algorithm
Max-Planck Institut für Astrophysik,
2 Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, 80539 München, Germany
Received: 7 November 2013
Accepted: 22 October 2014
The analysis of astronomical images is a non-trivial task. The D3PO algorithm addresses the inference problem of denoising, deconvolving, and decomposing photon observations. Its primary goal is the simultaneous but individual reconstruction of the diffuse and point-like photon flux given a single photon count image, where the fluxes are superimposed. In order to discriminate between these morphologically different signal components, a probabilistic algorithm is derived in the language of information field theory based on a hierarchical Bayesian parameter model. The signal inference exploits prior information on the spatial correlation structure of the diffuse component and the brightness distribution of the spatially uncorrelated point-like sources. A maximum a posteriori solution and a solution minimizing the Gibbs free energy of the inference problem using variational Bayesian methods are discussed. Since the derivation of the solution is not dependent on the underlying position space, the implementation of the D3PO algorithm uses the nifty package to ensure applicability to various spatial grids and at any resolution. The fidelity of the algorithm is validated by the analysis of simulated data, including a realistic high energy photon count image showing a 32 × 32 arcmin2 observation with a spatial resolution of 0.1 arcmin. In all tests the D3PO algorithm successfully denoised, deconvolved, and decomposed the data into a diffuse and a point-like signal estimate for the respective photon flux components.
Key words: methods: data analysis / methods: numerical / methods: statistical / techniques: image processing / gamma rays: general / X-rays: general
A copy of the code is available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (220.127.116.11) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/574/A74
© ESO, 2015
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