![]() ![]() As our training set, we use the simulation library and PCA basis employed in Medeiros et al. In this Letter, we employ PRIMO to reconstruct the image of the black hole in the center of the M87 galaxy based on the 2017 EHT data. Although, in general, decompositions used for dictionary learning do not need to be orthogonal or sparse, PCA does in fact lead to such a decomposition and enables an efficient dimensionality reduction, i.e., requiring a small number of components to fit the data. 2014 for a review of dictionary learning applied to image denoising). In machine-learning terms, the use of PCA to characterize the GRMHD training set as a sparse orthogonal basis is an example of dictionary learning (see, e.g., Shao et al. Even though we do not impose positivity on the final image, it emerges naturally in the PRIMO reconstructions. The PCA components themselves contain both positive and negative values. In contrast, PCA finds correlations between different regions in Fourier space in the training data, which allows PRIMO to generate physically motivated inferences for the unobserved Fourier components. General-purpose imaging algorithms, such as those used in prior EHT publications, rely on regularizers that, e.g., maximize entropy, minimize gradients, require positivity, and/or prefer compact sources, in order to fill the regions of the Fourier domain where there are no data. 2018 for an earlier exploration of PCA applied to GRMHD simulations). 2023 for details on PRIMO and Medeiros et al. PRIMO then uses a Markov Chain Monte Carlo (MCMC) approach to sample the space of linear combinations of the Fourier transforms of a number of PCA components while minimizing a loss function that compares the resulting interferometric maps to the EHT data (see Medeiros et al. In this approach, we apply principal components analysis (PCA) to a large library of high-fidelity, high-resolution general relativistic magnetohydrodynamic (GRMHD) simulations and obtain an orthogonal basis of image components. ![]() The robustness of the ring-like shapes of the images generated with model-agnostic methods motivates the use of principal-component interferometric modeling ( PRIMO), a novel image-reconstruction algorithm that addresses the challenges of millimeter-wave interferometry with sparse arrays by training the algorithm on an extensive suite of simulated images of accreting black holes (Medeiros et al. Extensive care was taken by the EHT collaboration to rigorously demonstrate that the ring morphology was uniquely required by the data (Event Horizon Telescope Collaboration et al. Those algorithms did not assume ring-like images and could easily have reconstructed a broad range of morphologies. ![]() ![]() The use of several general-purpose imaging algorithms, for example, was motivated by a desire to reconstruct an image that was consistent with the EHT data while remaining model-agnostic. In such situations, special care is needed to assess the impact of imaging algorithms and sparse interferometric data on the final set of images that can be reconstructed from it.Ī cornerstone of the EHT data analysis strategy was the use of several independent analysis methods, each with different priorities, assumptions, and choices, to ensure that the EHT results were robust to these differences. Despite this global reach, the sparse interferometric coverage of the EHT array (especially during the 2017 observations that have been used for all of the publications to date) makes the already complex problem of interferometric image reconstruction particularly challenging. The exceptional resolution achieved by the EHT is made possible by an array of telescopes spanning the Earth and operating as a very long baseline interferometer (VLBI Event Horizon Telescope Collaboration et al. 2019a, 2019b, 2019c, 2019d, 2019e, 2019f) and of Sagittarius A*, the Galactic Center black hole (Event Horizon Telescope Collaboration et al. The Event Horizon Telescope (EHT) 2017 observations provided high-sensitivity data over long baselines and resulted in the first horizon-scale images of the black hole in M87 (Event Horizon Telescope Collaboration et al. ![]()
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