We will discuss a fast, randomized approximate nearest neighbor algorithm (joint work with Andrei Osipov and Vladimir Rokhlin) and discuss applications to imaging problems, where nearest neighbor calculations are often a computational bottleneck. In the first part of the lecture I will discuss the algorithm and applications related to imaging. Part two of the lecture will be given by Zhizhen Zhao (Princeton). She will describe some projects in Amit Singer´s group where nearest neighbor problems appear in Cryo-EM, and where our algorithm is used.