D³PO: Denoising, Deconvolving, and Decomposing Photon Observations

A common problem for scientists analysing astronomical images is the separation of diffuse and point-like components. This analysis has now become easier: scientists at the Max Planck Institute for Astrophysics have recently published the D³PO algorithm, which removes noise effects and instrumental artefacts from the observed images, while simultaneously separating diffuse and point-like contributions.

Fig. 1: Simulated observation showing a 32 × 32 arcmin2 patch of the sky with a resolution of 0.1 arcmin.

Fig. 2: Reconstruction of the point-like photon flux, where each marker indicates a source, and its gray scale the corresponding flux.

Fig. 3: Reconstruction of the diffuse photon flux in which noise and instrumental artefacts have been removed.

Modern observatories provide raw images of the sky with high spatial resolution. In the X-ray and gamma-ray domain, individual photons are collected and depicted in photon count images. Since the number of photons detected is random to a certain degree, the raw image suffers from granularity due to the so-called shot noise. Further, an inhomogeneous sky exposure - especially for larger area surveys - and other instrumental effects leave unwanted imprints in the observational data. Imperfect instrument optics can, for example, cause point sources to be spread out so that they appear as smeared out blobs in the raw image. Furthermore, the sky emission is often an overlay of emission from different sources. Distinguishing between them on the image is ambiguous as it is often not clear from which of the sources a particular photon originates. It is therefore a real challenge to extract the original, astrophysical information contained in these noisy images and to sharpen them to high resolution.

To refine such raw images and reconstruct the original emission sources as reliably as possible, researchers from Garching have now developed a novel, intelligent imaging algorithm, which denoises, deconvolves, and decomposes photon observations — thus the name "D³PO". The removal or suppression of noise is commonly denoted as "denoising". In case of photon count images, this requires that the shot noise statistics is taken fully into account. "Deconvolution" in this context denotes the rectification of instrumental artefacts such as by imperfect optics. Spread out point sources are hereby remapped and sharpened to a single position on the image. Finally, "decomposition" is the separation of the photon count image into two different images, one for the extended and one for the point-like sources. The distinction between these morphologically different components is the most difficult task since the algorithm needs to decide on how to split the observed photons into the two possible source classes.

In order to achieve all this simultaneously, the D³PO algorithm relies on probabilistic inference that considers and weighs virtually all possible images of the sky while taking into account the raw photon image and all available a priori knowledge of how the sky could look like. For example, from the knowledge of how the observatory works, one has a decent idea of how a point source should look like in the raw image. Given an observation, one can judge how likely it is that a certain feature is a point source, diffuse emission, or just shot noise. This probabilistic reasoning has been designed using the framework of linkPfeil.gifInformation Field Theory, which provides a convenient language for the derivation of optimal imaging methods.

The images delivered by the D³PO algorithm are not only cured from noise and instrumental artefacts, but also provide a separation of the photon flux into extended and point-like sources. This is crucial for analysing high energy observations with respect to the astrophysical nature of the emission. On the one hand, extended emission regions, such as galactic clouds, galaxy clusters, or unresolved cosmic background emission, can be studied in the images without blooming point sources. And on the other hand, the analysis of point sources, like neutron stars and quasi-stellar objects (so-called quasars), can be carried out in images, where the background has been removed.

The D³PO algorithm is currently applied to data from the Chandra X-ray observatory and the Fermi gamma-ray space telescope at the Max Planck Institute for Astrophysics. The resulting images will hopefully provide the astrophysical community with a sharpened view on the high energy Universe.

Marco Selig, Torsten Enßlin, and Hannelore Hämmerle


The D³PO algorithm has been developed by Marco Selig at the Max Planck Institute for Astrophysics. Marco Selig is currently a PhD student in the research group of Torsten Enßlin and investigates information field theory-based imaging methods for high-energy astrophysics. His implementation of the D³PO algorithm will be released to the public in the near future.


Marco Selig and Torsten A. Enßlin, "Denoising, Deconvolving, and Decomposing Photon Observations", submitted to Astronomy & Astrophysics, linkPfeilExtern.gifhttp://arxiv.org/abs/1311.1888