  Imaging circumstellar disks in the near-infrared provides unprecedented
information about the formation and evolution of planetary systems. However,
current post-processing techniques for high-contrast imaging using ground-based
telescopes have a limited sensitivity to extended signals and their morphology
is often plagued with strong morphological distortions. Moreover, it is
challenging to disentangle planetary signals from the disk when the two
components are close or intertwined. We propose a pipeline that is capable of
detecting a wide variety of disks and preserving their shapes and flux
distributions. By construction, our approach separates planets from disks.
After analyzing the distortions induced by the current angular differential
imaging (ADI) post-processing techniques, we establish a direct model of the
different components constituting a temporal sequence of high-contrast images.
In an inverse problem framework, we jointly estimate the starlight residuals
and the potential extended sources and point sources hidden in the images,
using low-complexity priors for each signal. To verify and estimate the
performance of our approach, we tested it on VLT/SPHERE-IRDIS data, in which we
injected synthetic disks and planets. We also applied our approach on
observations containing real disks. Our technique makes it possible to detect
disks from ADI datasets of a contrast above $3\times10^{-6}$ with respect to
the host star. As no specific shape of the disks is assumed, we are capable of
extracting a wide diversity of disks, including face-on disks. The intensity
distribution of the detected disk is accurately preserved and point sources are
distinguished, even close to the disk.
