  A recent trend in the signal/image processing literature is the optimization
of Fourier sampling schemes for specific datasets of signals. In this paper, we
explain why choosing optimal non Cartesian Fourier sampling patterns is a
difficult nonconvex problem by bringing to light two optimization issues. The
first one is the existence of a combinatorial number of spurious minimizers for
a generic class of signals. The second one is a vanishing gradient effect for
the high frequencies. We conclude the paper by showing how using large datasets
can mitigate first effect and illustrate experimentally the benefits of using
stochastic gradient algorithms with a variable metric.
