  The Event Horizon Telescope (EHT) has produced images of the plasma flow
around the supermassive black holes in Sgr A* and M87* with a resolution
comparable to the projected size of their event horizons. Observations with the
next-generation Event Horizon Telescope (ngEHT) will have significantly
improved Fourier plane coverage and will be conducted at multiple frequency
bands (86, 230, and 345 GHz), each with a wide bandwidth. At these frequencies,
both Sgr A* and M87* transition from optically thin to optically thick.
Resolved spectral index maps in the near-horizon and jet-launching regions of
these supermassive black hole sources can constrain properties of the emitting
plasma that are degenerate in single-frequency images. In addition, combining
information from data obtained at multiple frequencies is a powerful tool for
interferometric image reconstruction, since gaps in spatial scales in
single-frequency observations can be filled in with information from other
frequencies. Here we present a new method of simultaneously reconstructing
interferometric images at multiple frequencies along with their spectral index
maps. The method is based on existing Regularized Maximum Likelihood (RML)
methods commonly used for EHT imaging and is implemented in the eht-imaging
Python software library. We show results of this method on simulated ngEHT data
sets as well as on real data from the VLBA and ALMA. These examples demonstrate
that simultaneous RML multi-frequency image reconstruction produces
higher-quality and more scientifically useful results than is possible from
combining independent image reconstructions at each frequency.
