Recovering Signals with Irregular Sampling

Abstract

In order to store and transmit a continuous signal, it is often sampled at discrete points. These discrete points may then be used in order to reconstruct the original signal, often using dual frame pairs. However, many reconstruction algorithms assume the signal is sampled at regular intervals, which may not be a valid assumption in practice. Previous work has been able to reconstruct such signals under certain conditions by erasing the data sampled at non-regular intervals, but this strategy fails when many points have been sampled irregularly. We develop an algorithm to achieve (theoretically) perfect reconstruction of a signal which has been sampled at nearly regular intervals without erasing any data points.