geom_tile不均匀地间隔的y值(例如2 ^ X)

I want to recreate an "image" plot in ggplot (because of some other aspects of the package). However, I'm facing a problem caused by my y-scale, which is defined by unequally but logically spaced values, e.g. I would have z values for y = 2,4,8,16,32. This causes the tiles to not be equally large, so I have these white bands in my figure. I can solve this by transforming the y values in a factor, but I don't want to do this because I'm also trying to plot other geom objects on the figure which require a numeric scale. This clearifies my problem a bit:I want to recreate an "image" plot in ggplot (b