Context. Polarimetric imaging is one of the most effective techniques for high-contrast imaging and characterization of circumstellar environments. These environments can be characterized through direct-imaging polarimetry at nearinfrared wavelengths. The Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE)/IRDIS instrument installed on the Very Large Telescope in its dual-beam polarimetric imaging (DPI) mode, offers the capability to acquire polarimetric images at high contrast and high angular resolution. However dedicated image processing is needed to get rid of the contamination by the stellar light, of instrumental polarization effects, and of the blurring by the instrumental point spread function. Aims. We aim to reconstruct and deconvolve the near-infrared polarization signal from circumstellar environments. Methods. We use observations of these environments obtained with the high-contrast imaging infrared polarimeter SPHERE-IRDIS at the Very Large Telescope (VLT). We developed a new method to extract the polarimetric signal using an inverse approach method that benefits from the added knowledge of the detected signal formation process. The method includes weighted data fidelity term, smooth penalization, and takes into account instrumental polarization Results. The method enables 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 capability to use incomplete polarimetry cycles which enhance the sensitivity of the observations. The method improves the overall performances in particular for low SNR/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 SNR, 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 to construct scattering phase functions.