  Context: Interferometric imaging is algorithmically and computationally
challenging as there is no unique inversion from the measurement data back to
the sky maps, and the datasets can be very large. Many imaging methods already
exist, but most of them focus either on the accuracy or the computational
aspect. Aims: This paper aims to reduce the computational complexity of the
Bayesian imaging algorithm resolve, enabling the application of Bayesian
imaging for larger datasets. Methods: By combining computational shortcuts of
the CLEAN algorithm with the Bayesian imaging algorithm resolve we developed an
accurate and fast imaging algorithm which we name fast-resolve. Results: We
validate the accuracy of the presented fast-resolve algorithm by comparing it
with results from resolve on VLA Cygnus A data. Furthermore, we demonstrate the
computational advantages of fast-resolve on a large MeerKAT ESO 137-006 dataset
which is computationally out of reach for resolve. Conclusions: The presented
algorithm is significantly faster than previous Bayesian imaging algorithms,
broadening the applicability of Bayesian interferometric imaging. Specifically
for the single channel VLA Cygnus A datasets fast-resolve is about $144$ times
faster than resolve. For the MeerKAT dataset with multiple channels the
computational speedup of fast-resolve is even larger.
