Context. Polarimetric imaging is one of the most effective techniques for the high-contrast imaging and characterization of circumstellar environments. These environments can be characterized through direct-imaging polarimetry at near-infrared wavelengths. The Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE)/IRDIS instrument, installed on the Very Large Telescope (VLT) in its dual-beam polarimetric imaging mode, offers the capability to acquire polarimetric images at high contrast and high angular resolution. However, dedicated image processing is needed to eliminate the contamination from the stellar light, instrumental polarization effects, and blurring from the instrumental point spread function.Aims. We aim to reconstruct and deconvolve the near-infrared polarization signal from circumstellar environments.Methods. We used observations of these environments obtained with the high-contrast imaging infrared polarimeter SPHERE-IRDIS at the VLT. We developed a new way to extract the polarimetric signal using an inverse approach method that benefits from the additional knowledge of the detected signal formation process. The method includes a weighted data fidelity term and smooth penalization, and it takes the instrumental polarization into account.Results. This method enables us to accurately measure the polarized intensity and angle of linear polarization of circumstellar disks by taking into account the noise statistics and the convolution by the instrumental point spread function. It has the capacity to use incomplete polarimetry cycles, which enhance the sensitivity of the observations. The method improves the overall performances in particular for instances of both low signal-to-noise (S/N) and small polarized flux compared to standard methods.Conclusions. By increasing the sensitivity and including deconvolution, our method will allow for more accurate studies of these disks morphology, especially in the innermost regions. It also will enable more accurate measurements of the angle of linear polarization at low S/N, which would lead to in-depth studies of dust properties. Finally, the method will enable more accurate measurements of the polarized intensity, which is critical for the construction of scattering phase functions.