Jet colormap to grayscale

Hello, I am looking to convert an image saved with the jet colormap to grayscale. I tried to play a bit with the color module of skimage, but for the moment I couldn't manage to to map the jet colormap to linearly go from dark to light shades of gray. The main problem when applying a basic rgb2gray conversion is that the min/max values (blue and red) converge to the same dark value in the grayscale image, while the mid-range values (yellow/green) become the brightest. Do someone has any trick to convert a "jet image" to grayscale? Thanks a lot Guillaume PS: I have attached a picture as an example if you're willing to play with it ;)