Filtering by Plotted Point Density

Consider the picture below. You'll notice that a lot of the data is very dense, i.e. if you drew a unit circle around any point in that area you'd be more likely to find a greater number of points within it, and a lot of it is not dense at all. I want to get rid of, i.e. 'de-plot' the latter kind of point.

In this particular example, I'd want to (roughly) ignore data where x<70, x>110, y>150. But my data won't always be so well organised, and I'll be dealing with large stacks at a time, so I want this filtering to be done by point density. How do I achieve this?

Thank you for any help!