Theoretical Foundation of Black Hole Image Reconstruction using PRIMO

A new image-reconstruction algorithm, PRIMO, applied to the interferometric data of the M87 black hole collected with the Event Horizon Telescope (EHT), resulted in an image that reached the native resolution of the telescope array. PRIMO is based on learning a compact set of image building blocks obtained from a large library of high-fidelity, physics-based simulations of black hole images. It uses these building blocks to fill the sparse Fourier coverage of the data that results from the small number of telescopes in the array. In this paper, we show that this approach is readily justified. Since the angular extent of the image of the black hole and of its inner accretion flow is finite, the Fourier space domain is heavily smoothed, with a correlation scale that is at most comparable to the sizes of the data gaps in the coverage of Fourier space with the EHT. Consequently, PRIMO or other machine-learning algorithms can faithfully reconstruct the images without the need to generate information that is unconstrained by the data within the resolution of the array. We also address the completeness of the eigenimages and the compactness of the resulting representation. We show that PRIMO provides a compact set of eigenimages that have sufficient complexity to recreate a broad set of images well beyond those in the training set.