Here's a a less destructive attempt. I gave up on getting entirely rid of the ripple in the background, but instead just tried to nuke the red dots.
(full version)
http://www.cs.rice.edu/~dwallach/photo/gertandmarsh2.jpgI'm sure cybjorg could push it even farther. If you wanted to get more serious, you'd try to find a tool that would let you transform the image to frequency space, where all of this texture would yield noise within a fairly narrow spectrum band where it would then be much easier to remove. I actually found an
FFT plugin for Photoshop, but the resulting images from a small amount of dorking around are, well, not exactly what you're looking for. There are commercial "texture removal" tools that would probably do a better job, if you really, really wanted to solve the problem...