  Despite their importance as subfields of mathematics and engineering, signal
and image processing have not received much attention in the field of quantum
computation. Cross-correlations are instrumental to all the aforementioned
fields. In this article we help fill this void by providing two quantum
algorithms, one for computing and storing cross-correlations, and one for
implementing the expectation maximization maximum likelihood algorithm. In
addition we show that the quantum expectation maximization maximum likelihood
algorithm has a quadratic speed-up compared to the classical analog.
