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tokens: difficult to provide because we have little prior information on it. However, a parsimonious parametric model of the PSF is suited for deconvolution processes (Drummond 1998 ; Markham Conchello 1999 ; Fétick et al. 2019a ). It is thus more efficient to parametrize the PSF using the available information on the observing system. The PSF model developed in Fétick et al. ( 2019b ) is adapted to AO-corrected images as it is able to describe both the coherent core and the turbulent halo of the AO-corrected PSF. Even with the strong prior of a parsimonious PSF parametrization, the joint maximum a posteriori estimator is not ensured to converge towards a satisfactory result. Indeed, the degeneracy of this estimator was demonstrated by Blanco Mugnier ( 2011 ) with a linear combination of PSFs for application to biomedical imaging. In this paper, we show that the joint estimator is also degenerated with a non-linear PSF model, although adapted to astronomical imaging. Because of the drawbacks of the joint estimator, we consider another method, which is the marginal estimator (Berger, Liseo Wolpert 1999 ; Blanc, Mugnier Idier 2003 ; Levin et al. 2009 ). This method consists of integrating – marginalizing – the object out of the problem to estimate only the PSF parameters. This estimator is asymptotically consistent and non-biased (Lehmann 1983 ) when the number of data or the signal-to-noise ratio (S/N) increase. We apply this method to our astronomical case in order to estimate the PSF parameters. The PSF is then used in a conventional (non-blind and non-myopic) deconvolution to estimate the object. In Section 2 , we explain the reasons for our choice of a parametric PSF model adapted to AO-corrected images. The first approach would be to use this parametric model to perform joint estimation. In Section 3 , we show that the deconvolution based on a joint estimation of the PSF and the object does not converge towards the correct solution in spite of the parametric PSF model introduced. Thus, we consider the marginalized approach in Section 4 . We study the effect of the S/N and the supervision level on the PSF estimation and image deconvolution. We show that this method can be adapted for blind deconvolution, with an example using astronomical images from the Spectro-Polarimetric High-contrast Exoplanet Research (SPHERE)/Zurich Imaging Polarimeter (Zimpol) on the Very Large Telescope (Beuzit et al. 2019 ). Finally, we conclude in Section 5 . 2 PSF AND IMAGING MODELS 2.1 PSF model Because ofhighly variable atmospheric conditions and the complexity of the AO correction, the PSF must be estimated for each observation. The simple method of estimating a PSF on a bright star is not possible for many observational cases, especially for observation of rsesolved objects in a small field of view. The PSF must be estimated with another method in order to be able to perform post-processing techniques on the image. This estimation might be based on telemetry or on