Division of focal plane (DoFP) polarization imaging sensors have the distinct advantage of acquiring temporally synchronized Stokes vector in one scene. The sensors' spatially modulated arrangement of a micropolarization array results in loss of spatial resolution and instantaneous field-of-overview errors. Polarization demosaicking (PDM) methods are often utilized to address these drawbacks and achieve the goal of recovering missing polarization information. In this paper, we propose minimized Laplacian polarization residual interpolation for PDM. The Laplacian energy is introduced to improve the interpolation accuracy. We employ interchannel correlation and a guided filter to generate precise tentative estimates and the interpolation performed in the residual domain, where the residuals are the differences between observed values and tentative estimates. Experiments demonstrate that the proposed algorithm provides superior performance in terms of mean average error and peak signal-to-noise ratio.