A curves (ctrl-m) with these points should work good enough:
39, 0
69, 62
95, 95
160, 163
215, 225
231, 255
(also make sure it is on Light (0-255) mode not Pigment/Ink%)
Some details will be lost in the near-white and near-black areas, so maybe also use a small denoise and less black/white...