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Bayesian and Machine Learning Methods in the Big Data Era for Astronomical Imaging^{ †}

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## Abstract

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## 1. Introduction

## 2. ALMA and the Ill-Posed Inverse Problem

#### 2.1. RESOLVE for Bayesian Signal Inference

#### 2.2. Deep Learning for Fast Image Reconstruction

## 3. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Wootten, A.; Thompson, A.R. The Atacama large millimeter/Submillimeter array. Proc. IEEE
**2009**, 97, 1463–1471. [Google Scholar] [CrossRef] [Green Version] - Cortes, P.; Remijan, A.; Biggs, A.; Dent, B.; Carpenter, J.; Fomalont, E.; Hales, A.; Kameno, S.; Mason, B.; Philips, N.; et al. ALMA Cycle 8 2021 Technical Handbook; Atacama Large Millimeter/Submillimeter Array (ALMA): Antofagasta, Chile, 2021. [Google Scholar] [CrossRef]
- Huang, Y.D.T.; Morata, O.; Koch, P.M.; Kemper, C.; Hwang, Y.J.; Chiong, C.C.; Ho, P.; Chu, Y.H.; Huang, C.D.; Liu, C.T.; et al. The Atacama large millimeter/sub-millimeter array band-1 receiver. In Modeling, Systems Engineering, and Project Management for Astronomy VI; Angeli, G.Z., Dierickx, P., Eds.; SPIE: Bellingham, WA, USA, 2016; Volume 9911, p. 99111V. [Google Scholar] [CrossRef] [Green Version]
- Yagoubov, P.; Mroczkowski, T.; Belitsky, V.; Cuadrado-Calle, D.; Cuttaia, F.; Fuller, G.A.; Gallego, J.D.; Gonzalez, A.; Kaneko, K.; Mena, P.; et al. Wideband 67–116 GHz receiver development for ALMA Band 2. A&A
**2020**, 634, A46. [Google Scholar] [CrossRef] [Green Version] - Carpenter, J.; Iono, D.; Kemper, F.; Wootten, A. The ALMA Development Program: Roadmap to 2030. arXiv
**2020**, arXiv:2001.11076. [Google Scholar] [CrossRef] - McMullin, J.P.; Waters, B.; Schiebel, D.; Young, W.; Golap, K. CASA Architecture and Applications. In Astronomical Data Analysis Software and Systems XVI; Shaw, R.A., Hill, F., Bell, D.J., Eds.; SPIE: Bellingham, WA, USA, 2007; Volume 376, p. 127. [Google Scholar]
- Taylor, G.B.; Carilli, C.L.; Perley, R.A. Synthesis Imaging in Radio Astronomy II; Astronomical Society of the Pacific: San Francisco, CA, USA, 1999; Volume 180. [Google Scholar]
- Guglielmetti, F.; Villard, E.; Fomalont, E. Bayesian Reconstruction through Adaptive Image Notion. Proceedings
**2019**, 33, 21. [Google Scholar] [CrossRef] [Green Version] - Junklewitz, H.; Bell, M.R.; Selig, M.; Enßlin, T.A. RESOLVE: A new algorithm for aperture synthesis imaging of extended emission in radio astronomy. Astron. Astrophys.
**2016**, 586, A76. [Google Scholar] [CrossRef] [Green Version] - Greiner, M.; Vacca, V.; Junklewitz, H.; Enßlin, T.A. fastRESOLVE: Fast Bayesian imaging for aperture synthesis in radio astronomy. arXiv
**2016**, arXiv:1605.04317. [Google Scholar] - Arras, P.; Knollmüller, J.; Junklewitz, H.; Enßlin, T.A. Radio Imaging with Information Field Theory. arXiv
**2018**, arXiv:1803.02174. [Google Scholar] - Enßlin, T.A.; Frommert, M.; Kitaura, F.S. Information field theory for cosmological perturbation reconstruction and nonlinear signal analysis. Phys. Rev. D
**2009**, 80, 105005. [Google Scholar] [CrossRef] [Green Version] - Enßlin, T. Information field theory. AIP Conf. Proc.
**2013**, 1553, 184. [Google Scholar] [CrossRef] [Green Version] - Arras, P.A. Radio Interferometry with Information Field Theory. Ph.D. Thesis, Faculty of Physics, Ludwig-Maximilians-Universität München, München, Germany, January 2021. [Google Scholar]
- Reinecke, M.; Steininger, T.; Selig, M. NIFTy—Numerical Information Field TheorY. Version nifty4. 5 February 2018. Available online: https://gitlab.mpcdf.mpg.de/ift/nifty/-/tree/NIFTy_4#nifty4 (accessed on 18 July 2022).
- Arras, P.; Bester, H.L.; Perley, R.A.; Leike, R.; Smirnov, O.; Westermann, R.; Enßlin, T.A. Comparison of classical and Bayesian imaging in radio interferometry. Astron. Astrophys.
**2021**, 646, A84. [Google Scholar] [CrossRef] - Tychoniec, L. Bayesian statistics approach to imaging of aperture synthesis data: RESOLVE meets ALMA. In Proceedings of the International Conference on Bayesian and Maximum Entropy Methods in Science and Engineering, Paris, France, 18–22 July 2022. Number 67. [Google Scholar]
- Brogan, C.L.; Pérez, L.M.; Hunter, T.R.; Dent, W.R.F.; Hales, A.S.; Hills, R.E.; Corder, S.; Fomalont, E.B.; Vlahakis, C.; Asaki, Y.; et al. The 2014 ALMA long baseline campaign: First results from high angular resolution observations toward the HL Tau region. Astrophys. J. Lett.
**2015**, 808, L3. [Google Scholar] [CrossRef] - Realizing the potential of astrostatistics and astroinformatics. Bull. Am. Astron. Soc.
**2019**, 51, 233. - Delli Veneri, M. 3D Detection and Characterisation of ALMA Sources through Deep Learning. MNRAS, 2022, submitted.
- Carniani, S.; Marconi, A.; Biggs, A.; Cresci, G.; Cupani, G.; D’Odorico, V.; Humphreys, E.; Maiolino, R.; Mannucci, F.; Molaro, P.; et al. Strongly star-forming rotating disks in a complex merging system at z = 4.7 as revealed by ALMA. Astron. Astrophys.
**2013**, 559, A29. [Google Scholar] [CrossRef] - Siemiginowska, A.; Kuhn, M.; Graham, M.; Mahabal, A.A.; Taylor, S.R. The Next Decade of Astroinformatics and Astrostatistics. Bull. Am. Astron. Soc.
**2019**, 51, 355. [Google Scholar]

**Figure 1.**(

**a**) The ALMA correlator in the ALMA array operation site (AOS) technical building is composed of four identical quadrants with over $134\times {10}^{6}$ processors, performing up to $17\times {10}^{24}$ operations/s (Image credit: ESO). (

**b**) A panoramic view of the ALMA array, located at an elevation of 5000 m on the Chajnantor Plateau in the Chilean Andes. The AOS is the small building left of picture center. The tight clump of antennas near the image center is the ACA (Image credit: JAO).

**Figure 2.**The application of RESOLVE on SV data, HL Tau, and continuum image at 1.3 mm (233 GHz), using only one out of four 1.8275 GHz spectral window composed by 128 channels. (

**a**) Image reconstruction of HL Tau in units of (mJy/beam) indicating the posterior mean (upper) and the relative pixel-wise posterior uncertainty (lower). (

**b**) The estimated mean spatial correlation, or the posterior power spectrum of the reconstructed image (upper) and its uncertainty (lower).

**Figure 3.**Schematic view of the DL pipeline used within the 3D detection and characterization of ALMA sources [20], with the numbers showing the logic flow of the data.

**Figure 4.**(

**a**) [CII] line emission observed at 0.9 mm (334 GHz): integrated intensity map from ALMA dirty cube in BR1202-0725, a binary system observed edge-on and with the galaxies moving along the line of sight. (

**b**) The predicted image with the DL Pipeline.

**Figure 5.**Application of Blobs Finder (part of the DL Pipeline) to ALMA simulated dirty images. (

**a**–

**c**), the simulated ALMA dirty cube, Blobs Finder prediction, and Sky model, respectively. These are integrated intensity maps. The red boxes indicate the lines found by Blobs Finder. Spectral analysis is performed on each detected line by ResNets in a subsequent stage.

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## Share and Cite

**MDPI and ACS Style**

Guglielmetti, F.; Arras, P.; Delli Veneri, M.; Enßlin, T.; Longo, G.; Tychoniec, L.; Villard, E.
Bayesian and Machine Learning Methods in the Big Data Era for Astronomical Imaging. *Phys. Sci. Forum* **2022**, *5*, 50.
https://doi.org/10.3390/psf2022005050

**AMA Style**

Guglielmetti F, Arras P, Delli Veneri M, Enßlin T, Longo G, Tychoniec L, Villard E.
Bayesian and Machine Learning Methods in the Big Data Era for Astronomical Imaging. *Physical Sciences Forum*. 2022; 5(1):50.
https://doi.org/10.3390/psf2022005050

**Chicago/Turabian Style**

Guglielmetti, Fabrizia, Philipp Arras, Michele Delli Veneri, Torsten Enßlin, Giuseppe Longo, Lukasz Tychoniec, and Eric Villard.
2022. "Bayesian and Machine Learning Methods in the Big Data Era for Astronomical Imaging" *Physical Sciences Forum* 5, no. 1: 50.
https://doi.org/10.3390/psf2022005050