Bayesian statistics approach to imaging of aperture synthesis data RESOLVE meets ALMA._2

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Proceedings

Bayesian statistics approach to imaging of aperture

synthesis data: RESOLVE meets ALMA.†

Lukasz Tychoniec1,∗, Fabrizia Guglielmetti1, Philipp Arras2, Torsten Enßlin2, Eric Villard1

1European Southern Observatory, Karl-Schwarzschildstr. 2, Garching D-85748, Germany

2Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str.1, Garching D-85748, Germany

*lukasz.tychoniec@eso.org

† Submitted to International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and

Engineering, IHP, Paris, July 18-22, 2022.

Received: June 2022; Accepted: -; Published: -

Abstract:

The Atacama Large Millimeter/submillimeter Array (ALMA) is currently revolutionizing

observational astrophysics. The aperture synthesis technique provides angular resolution otherwise

unachievable with the conventional single-aperture telescope. However, recovering the image from the

inherently undersampled data is a challenging task. The

clean

algorithm [

] has proven successful and

reliable and is commonly used in imaging the interferometric observations. It is not, however, free of

limitations. Point-source assumption, central to the

clean

is not optimal for the extended structures of

molecular gas recovered by ALMA. Additionally, negative ﬂuxes recovered with

clean

are not physical.

This begs to search for alternatives that would be better suited for speciﬁc science cases. We present the

recent developments in imaging ALMA data using Bayesian inference techniques, namely the

resolve

algorithm [

]. This algorithm, based on information ﬁeld theory [

], has been already successfully applied

to image the Very Large Array data [

]. We compare the capability of both

clean

and

resolve

to recover

known sky signal, convoluted with the simulator of ALMA observation data and we investigate the

problem with a set of actual ALMA observations.

Keywords: Bayesian Inference; Inference Methods; Image Analysis; Radio Astronomy

1. Introduction

1.1. Aperture synthesis

The Atacama Large Millimeter/submillimeter Array (ALMA) is revolutionizing observational

astrophysics. With its 66 antennas located on the Atacama desert it provided the sharpest ever images of

the submillimeter sky, for example, images of the protoplanetary disks at 1 au resolution [

]. In order to

obtain such a resolution at a distance to a nearby star-forming region at 1.3 mm a telescope diameter of

∼

15 km are needed. Since the construction challenges of such an antenna, especially if one would like to

make it steerable, are far beyond current technical capabilities, in radio astronomy domain we often turn

to aperture synthesis techniques, where instead of a single dish, a combination of smaller antennas is used,

and with interference of signal between each antennas a resolution compared to the a telescope of a size of

the greatest distance between the two antennas in an array (i.e. baseline) is achieved.

This does not come without a cost: sampling the baselines is never complete compared with a single

dish telescopes. This means we do not receive complete information at all baselines and therefore to create

an image of the sky we are operating with missing information.

Entropy 2022,0, 0; doi:10.3390/e0000000 www.mdpi.com/journal/entropy

arXiv:2210.02408v1 [astro-ph.IM] 5 Oct 2022

Entropy 2022,0, 0 2 of 9

A direct measurement of an interferometer is the interference pattern between two given antennas.

This pattern is related to the sky brightness observed by the antennas. The recorded complex value

called visibility is then a Fourier transform of the sky brightness, the quantity which observations aim

to recover. Therefore, a simpliﬁed imaging process consists of a (reverse) Fourier transformation of the

measured visibilities (while the non-measured visibilities are set to 0) to obtain ﬁrst approximation of the

sky brightness, the so-called dirty image [

]. Once this is achieved, it becomes apparent that even with

modern interferometer like ALMA with many baselines sampling the so-called UV plane we achieve a

rather poor quality image. Reﬁning this image is the topic of this work.

1.2. CLEAN as fa standard approach to the imaging of the interferometric data

A standard technique to improve the image quality of the interferometric observations has been

developed by Hogbom in 1974 [

] and is called

clean

Clean

makes use of the well-deﬁned point-spread

function of a given antenna conﬁguration. The algorithm identiﬁes the point sources in the initial dirty

image, point sources are then approximated with a delta function, convolved it with a dirty beam (i.e. the

assumed pattern that the point-source would create on the dirty image), scales it with brightness of the

suspected point source and subtracts the point-source patter from the dirty image. This is an iterative

process which ideally ends when all point sources are removed from the dirty image so that it consists

only of noise. [6]

One issue of

clean

that can be easily identiﬁed is in the assumption that the sky is composed of point

sources. This results in

clean

struggling with imaging of extended sky brightness structures. Several

modiﬁcations to the original

clean

algorithm have been implemented to mitigate this issue, such as

multi-scale clean which allows to set a point-source that would be a Gaussian rather than a delta function

[2,8].

There are several steps in the process of cleaning which can be modiﬁed to improve the process.

Masking is a method to restrict the area where the algorithm will look for point sources to a selected region

on the sky. Weighting allows to attribute different weights to different u,v scales, allowing for a trade-off

between resolution and sensitivity.

Although

clean

became a gold standard of the interferometric data imaging, producing many

stunning images of the astronomical objects its limitation beg to seek alternatives, especially in cases where

its assumptions are not met.

1.3. resolve algorithm and IFT

Imaging of the interferometric data can be presented as an inference problem, since we operate on

an incomplete measurement problem, trying to ﬁnd the true sky emission from the received data. Radio

Extended SOurces Lognormal deconVolution Estimator

resolve 1

[

] is designed in the Information

Field Theory (IFT) framework [

]. IFT enables to use Bayesian inference methods in the context of

mathematical framework of ﬁeld theory. This is well ﬁtted to the issue of imaging the sky brightness. IFT

algorithms are implemented in resolve through Python package NIFTy 2[11,12].

The measurement equation can be presented as:

d=R(s) + n

, where

is a response of the instrument

to the original physical signal (

), and

is noise. In the IFT framework, obtained data

is analyzed in

1https://gitlab.mpcdf.mpg.de/ift/resolve

2https://gitlab.mpcdf.mpg.de/ift/NIFTy

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ProceedingsBayesianstatisticsapproachtoimagingofaperturesynthesisdata:RESOLVEmeetsALMA.LukaszTychoniec1,,FabriziaGuglielmetti1,PhilippArras2,TorstenEnßlin2,EricVillard11EuropeanSouthernObservatory,Karl-Schwarzschildstr.2,GarchingD-85748,Germany2MaxPlanckInstituteforAstrophysics,Karl-Schwarzschild-...

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