  We address the problem of recovering signals from samples taken at their rate
of innovation. Our only assumption is that the sampling system is such that the
parameters defining the signal can be stably determined from the samples, a
condition that lies at the heart of every sampling theorem. Consequently, our
analysis subsumes previously studied nonlinear acquisition devices and
nonlinear signal classes. In particular, we do not restrict attention to
memoryless nonlinear distortions or to union-of-subspace models. This allows
treatment of various finite-rate-of-innovation (FRI) signals that were not
previously studied, including, for example, continuous phase modulation
transmissions. Our strategy relies on minimizing the error between the measured
samples and those corresponding to our signal estimate. This least-squares (LS)
objective is generally non-convex and might possess many local minima.
Nevertheless, we prove that under the stability hypothesis, any optimization
method designed to trap a stationary point of the LS criterion necessarily
converges to the true solution. We demonstrate our approach in the context of
recovering pulse streams in settings that were not previously treated.
Furthermore, in situations for which other algorithms are applicable, we show
that our method is often preferable in terms of noise robustness.
