Abstract In the context of extreme adaptive optics for large telescopes, we present the Kraken multi-frame blind deconvolution (MFBD) algorithm for processing high-cadence acquisitions, capable of providing 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 wave front at the entrance pupil. Under suitable physical constraints, numerical convergence is guaranteed by an iteration scheme starting from a compact MFBD, which provides a very robust initial guess that only employs a few frames. We describe the mathematics behind the process and report the high-resolution reconstruction of the spectroscopic binary α 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.