Extracting scientific data from .PNG/.JPEG image

I have to extract data from an intensity plot to use it in a simulation. The problem is that I have no information regarding the colormap which has been used except for a mere colorbar on the right.

I would like to be as accurate as possible as the image is low resolution and I suppose I would be already on thin ice if I were able to extract all the data. Nothing pops into my head despite very time consuming techniques, while I would like to rely on some built-in code to speed up the procedure.

Has anyone addressed such a problem before? Unfortunately I cannot publish the image due to copyright reasons.