  Imaging spectroscopy, i.e., the generation of spatially resolved count
spectra and of cubes of count maps at different energies, is one of the main
goals of solar hard X-ray missions based on Fourier imaging. For these
telescopes, so far imaging spectroscopy has been realized via the generation of
either count maps independently reconstructed at the different energy channels,
or electron flux maps reconstructed via deconvolution of the bremsstrahlung
cross-section. Our aim is to introduce the Regularized Imaging Spectroscopy
method (RIS), in which regularization implemented in the count space imposes a
smoothing constraint across contiguous energy channels, without the need to
deconvolve the bremsstrahlung effect. STIX records imaging data computing
visibilities in the spatial frequency domain. Our RIS is a sequential scheme in
which part of the information coded in the image reconstructed at a specific
energy channel is transferred to the reconstruction process at a contiguous
channel via visibility interpolation based on Variably Scaled Kernels. In the
case of STIX visibilities recorded during the November 11, 2022 flaring event,
we show that RIS is able to generate hard X-ray maps whose morphology smoothly
evolves from one energy channel to the contiguous one, and that from these maps
it is possible to infer spatially-resolved count spectra characterized by
notable numerical stability. We also show that the performances of this
approach are robust with respect to both the image reconstruction method and
the count energy channel utilized to trigger the sequential process. RIS is
appropriate to construct image cubes from STIX visibilities that are
characterized by a smooth behavior across count energies, thus allowing the
generation of numerically stable (and, thus, physically reliable) local count
spectra.
