The curvelet transform is a directional wavelet transform over R^n, which is

used to analyze functions that have singularities along smooth surfaces (Candes

and Donoho, 2002). I demonstrate how this can lead to new quantum algorithms. I

give an efficient implementation of a quantum curvelet transform, together with

two applications: a single-shot measurement procedure for approximately finding

the center of a ball in R^n, given a quantum-sample over the ball; and, a

quantum algorithm for finding the center of a radial function over R^n, given

oracle access to the function. I conjecture that these algorithms succeed with

constant probability, using one quantum-sample and O(1) oracle queries,

respectively, independent of the dimension n -- this can be interpreted as a

quantum speed-up. To support this conjecture, I prove rigorous bounds on the

distribution of probability mass for the continuous curvelet transform. This

shows that the above algorithms work in an idealized "continuous" model.