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Aims. The purpose of this paper is to describe a new post-processingalgorithm dedicated to the reconstruction of the spatial distribution of lightreceived from off-axis sources, in particular from circumstellar disks.  Methods. Built on the recent PACO algorithm dedicated to the detection ofpoint-like sources, the proposed method is based on the local learning of patchcovariances capturing the spatial fluctuations of the stellar leakages. Fromthis statistical modeling, we develop a regularized image reconstructionalgorithm (REXPACO) following an inverse problem approach based on a forwardimage formation model of the off-axis sources in the ADI sequences.  Results. Injections of fake circumstellar disks in ADI sequences from theVLT/SPHERE-IRDIS instrument show that both the morphology and the photometry ofthe disks are better preserved by REXPACO compared to standard postprocessingmethods like cADI. In particular, the modeling of the spatial covariancesproves usefull in reducing typical ADI artifacts and in better disentanglingthe signal of these sources from the residual stellar contamination. Theapplication to stars hosting circumstellar disks with various morphologiesconfirms the ability of REXPACO to produce images of the light distributionwith reduced artifacts. Finally, we show how REXPACO can be combined with PACOto disentangle the signal of circumstellar disks from the signal of candidatepoint-like sources.  Conclusions. REXPACO is a novel post-processing algorithm producingnumerically deblurred images of the circumstellar environment. It exploits thespatial covariances of the stellar leakages and of the noise to efficientlyeliminate this nuisance term.

REXPACO: an algorithm for high contrast reconstruction of the circumstellar environment by angular differential imaging