This paper appears in the most recent in issue of SIAM Review, and it is simply fantastic. It is well written and clear, and it judiciously limits the scope to fundamental concepts in statistical inverse problems. I recommend this to anyone interested in such ideas — both students and experienced researchers. In fact, I’m giving a lecture this evening to the UQ class on inverse problems, and I plan to both borrow heavily from its presentation and make it required reading for the class.
Here’s the link.