How to use a suitable color bar?

I have a picture which shows the magnitude of some value in terms of color, like this one:

https://www.dropbox.com/s/yoh0n9cqftvrtlz/bar.jpg?dl=0

The higher the magnitude, the more it looks red. However there are only a few points at the edge has very high values and most of the points have much lower values. If a colorbar with equal intervals is used the picture just looks blue throughout and the values in most areas cannot be distinguished.

Is it possible to set a colorbar that has, say, exponentially increasing intervals (or others) so that the center part can also show different colors?