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One of the major limitations of adaptive optics (AO) corrected image post-processing is the lack of knowledge on the system point spread function (PSF). The PSF is not always available as a direct imaging on isolated point like objects such as stars. Its prediction using AO telemetry also suffers from serious limitations and requires complex and yet not fully operational algorithms. A very attractive solution consists in a direct PSF estimation using the scientific images themselves thanks to blind or myopic post-processing approaches. We demonstrate that such approaches suffer from severe limitations when a joint restitution of object and PSF parameters is performed. As an alternative we propose here a marginalized PSF identification that overcomes this limitation. Then the PSF is used for image post-processing. Here we focus on deconvolution, a post-processing technique to restore the object, given the image and the PSF. We show that the PSF estimated by marginalisation provides good quality deconvolution. The full process of marginalized PSF estimation and deconvolution constitutes a successful blind deconvolution technique. It is tested on simulated data to measure its performance. It is also tested on experimental adaptive optics images of the asteroid 4-Vesta by VLT/SPHERE/Zimpol to demonstrate application to on-sky data.