We have experimentally investigated the enhancement in spatial resolution by image subtraction in mid-infrared central solid-immersion lens (c-SIL) microscopy. The subtraction exploits a first image measured with the c-SIL point-spread function (PSF) realized with a Gaussian beam and a second image measured with the beam optically patterned by a silicon π-step phase plate, to realize a centrally hollow PSF. The intense sides lobes in both PSFs that are intrinsic to the SIL make the conventional weighted subtraction methods inadequate. A spatial-domain filter with a kernel optimized to match both experimental PSFs in their periphery was thus developed to modify the first image prior to subtraction, and this resulted in greatly improved performance, with polystyrene beads 1.4 ± 0.1 µm apart optically resolved with a mid-IR wavelength of 3.4 µm in water. Spatial-domain filtering is applicable to other PSF pairs, and simulations show that it also outperforms conventional subtraction methods for the Gaussian and doughnut beams widely used in visible and near-IR microscopy.