  Regularized imaging spectroscopy was introduced for the construction of
electron flux images at different energies from count visibilities recorded by
the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). In this work
we seek to extend this approach to data from the Spectrometer/Telescope for
Imaging X-rays (STIX) on-board the Solar Orbiter mission. Our aims are to
demonstrate the feasibility of regularized imaging spectroscopy as a method for
analysis of STIX data, and also to show how such analysis can lead to insights
into the physical processes affecting the nonthermal electrons responsible for
the hard X-ray emission observed by STIX. STIX records imaging data in an
intrinsically different manner from RHESSI. Rather than sweeping the angular
frequency plane in a set of concentric circles (one circle per detector), STIX
uses $30$ collimators, each corresponding to a specific angular frequency. In
this paper we derive an appropriate modification of the previous computational
approach for the analysis of the visibilities observed by STIX. This approach
also allows for the observed count data to be placed into non-uniformly-spaced
energy bins. We show that the regularized imaging spectroscopy approach is not
only feasible for analysis of the visibilities observed by STIX, but also more
reliable. Application of the regularized imaging spectroscopy technique to
several well-observed flares reveals details of the variation of the electron
flux spectrum throughout the flare sources. We conclude that the
visibility-based regularized imaging spectroscopy approach is well-suited to
analysis of STIX data. We also use STIX electron flux spectral images to track,
for the first time, the behavior of the accelerated electrons during their path
from the acceleration site in the solar corona toward the chromosphere
