D$^3$PO - Denoising, Deconvolving, and Decomposing Photon Observations

TL;DR

The D3PO algorithm provides a probabilistic method for simultaneously denoising, deconvolving, and decomposing photon observations into diffuse and point-like components in astronomical images, validated on simulated data.

Contribution

It introduces a hierarchical Bayesian algorithm that uniquely separates diffuse and point-like photon fluxes from a single observation, adaptable to various spatial resolutions.

Findings

Successfully denoised, deconvolved, and decomposed simulated photon data.

Validated the algorithm on realistic high-energy photon images.

Demonstrated applicability across different spatial grids and resolutions.

Abstract

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 x 32 arcmin^2 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.