Optimization-based recovery from rate of innovation samples

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. As such, our analysis subsumes previously studied nonlinear acquisition devices and nonlinear signal classes. Our strategy relies on minimizing a least-squares (LS) objective, which is generally non-convex and might possess many local minima. We show, though, that under the stability hypothesis, any optimization method designed to trap a stationary point necessarily converges to the true solution. We demonstrate the usefulness of our approach in recovering finite-duration and periodic pulse streams.