master project?

A potential master project for my students next year inspired by an X validated question: given a Gaussian mixture density

with m known, the weights summing up to one, and the (prior) information that all means are within (-C,C), derive the parameters of this mixture from a sufficiently large number of evaluations of f. Pay attention to the numerical issues associated with the resolution.  In a second stage, envision this problem from an exponential spline fitting perspective and optimise the approach if feasible.