  Bolometric interferometry is a novel technique that has the ability to
perform spectral imaging. A bolometric interferometer observes the sky in a
wide frequency band and can reconstruct sky maps in several sub-bands within
the physical band in post-processing of the data. This provides a powerful
spectral method to discriminate between the cosmic microwave background (CMB)
and astrophysical foregrounds. In this paper, the methodology is illustrated
with examples based on the Q \& U Bolometric Interferometer for Cosmology
(QUBIC) which is a ground-based instrument designed to measure the B-mode
polarization of the sky at millimeter wavelengths. We consider the specific
cases of point source reconstruction and Galactic dust mapping and we
characterize the point spread function as a function of frequency. We study the
noise properties of spectral imaging, especially the correlations between
sub-bands, using end-to-end simulations together with a fast noise simulator.
We conclude showing that spectral imaging performance are nearly optimal up to
five sub-bands in the case of QUBIC.
