We address the problem of generalized sampling and reconstruction of finite-rate-of-innovation signals. Specifically, we consider the problem of sampling streams of Dirac impulses and propose a two-channel method that enables fast, local reconstruction under some suitable conditions. We also specify some acquisition kernels and give the associated reconstruction formulas. It turns out that these kernels can also be combined into one kernel, which can be employed in the single-channel sampling scenario. The single-kernel approach carries over all the advantages of the two-channel counterpart. Simulation results are presented to validate the theoretical calculations.