Non-uniform Random Sampling and Reconstruction in Signal Spaces with Finite Rate of Innovation

We consider non-uniform random sampling in a signal space with finite rate of innovation V2 generated by a series of functions phi=(phi lambda)lambda is an element of. A subset VR,delta 2(?,phi) of V2(?,phi) is consisting of functions concentrates at least 1-delta of the whole energy in a cube with side lengths R. Under mild assumptions on the generators and the probability distribution, we show that for R sufficiently large, taking O(Rdlog(Rd)) many samples with such the non-uniform distribution yields a sampling set for VR,delta 2(?,phi) with high probability. We impose compact support on the generators as an additional constraint for obtaining a reconstruction algorithm from non-uniform random sampling with high probability.