Title: Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope using Sparse Modeling,
Abstract: We propose a new imaging technique for radio and optical/infrared
interferometry. The proposed technique reconstructs the image from the
visibility amplitude and closure phase, which are standard data products of
short-millimeter very long baseline interferometers such as the Event Horizon
Telescope (EHT) and optical/infrared interferometers, by utilizing two
regularization functions: the $\ell_1$-norm and total variation (TV) of the
brightness distribution. In the proposed method, optimal regularization
parameters, which represent the sparseness and effective spatial resolution of
the image, are derived from data themselves using cross validation (CV). As an
application of this technique, we present simulated observations of M87 with
the EHT based on four physically motivated models. We confirm that $\ell_1$+TV
regularization can achieve an optimal resolution of $\sim 20-30$% of the
diffraction limit $\lambda/D_{\rm max}$, which is the nominal spatial
resolution of a radio interferometer. With the proposed technique, the EHT can
robustly and reasonably achieve super-resolution sufficient to clearly resolve
the black hole shadow. These results make it promising for the EHT to provide
an unprecedented view of the event-horizon-scale structure in the vicinity of
the super-massive black hole in M87 and also the Galactic center Sgr A*.