  Aims. The purpose of this paper is to describe a new post-processing
algorithm dedicated to the reconstruction of the spatial distribution of light
received from off-axis sources, in particular from circumstellar disks.
  Methods. Built on the recent PACO algorithm dedicated to the detection of
point-like sources, the proposed method is based on the local learning of patch
covariances capturing the spatial fluctuations of the stellar leakages. From
this statistical modeling, we develop a regularized image reconstruction
algorithm (REXPACO) following an inverse problem approach based on a forward
image formation model of the off-axis sources in the ADI sequences.
  Results. Injections of fake circumstellar disks in ADI sequences from the
VLT/SPHERE-IRDIS instrument show that both the morphology and the photometry of
the disks are better preserved by REXPACO compared to standard postprocessing
methods like cADI. In particular, the modeling of the spatial covariances
proves usefull in reducing typical ADI artifacts and in better disentangling
the signal of these sources from the residual stellar contamination. The
application to stars hosting circumstellar disks with various morphologies
confirms the ability of REXPACO to produce images of the light distribution
with reduced artifacts. Finally, we show how REXPACO can be combined with PACO
to disentangle the signal of circumstellar disks from the signal of candidate
point-like sources.
  Conclusions. REXPACO is a novel post-processing algorithm producing
numerically deblurred images of the circumstellar environment. It exploits the
spatial covariances of the stellar leakages and of the noise to efficiently
eliminate this nuisance term.
