  In the context of extreme adaptive optics (ExAO) for large telescopes, we
present the Kraken multi-frame blind deconvolution (MFBD) algorithm for
processing high-cadence acquisitions, capable to provide a diffraction-limited
estimation of the source brightness distribution. This is achieved by a data
modeling of each frame in the sequence driven by the estimation of the
instantaneous wavefront at the entrance pupil. Under suitable physical
contraints, numerical convergence is guaranteed by an iteration scheme starting
from a Compact MFBD (CMFBD) which provides a very robust initial guess which
only employs a few frames. We describe the mathematics behind the process and
report the high-resolution reconstruction of the spectroscopic binary {\alpha}
And (16.3 mas separation) acquired with the precursor of SHARK-VIS, the
upcoming high-contrast camera in the visible for the Large Binocular Telescope.
