We present an online algorithm for reconstructing a signal from a set of
non-uniform samples. By representing the signal using compactly supported basis
functions, we show how estimating the expansion coefficients using
least-squares can be implemented in a streaming manner: as batches of samples
over subsequent time intervals are presented, the algorithm forms an initial
estimate of the signal over the sampling interval then updates its estimates
over previous intervals. We give conditions under which this reconstruction
procedure is stable and show that the least-squares estimates in each interval
converge exponentially, meaning that the updates can be performed with finite
memory with almost no loss in accuracy. We also discuss how our framework
extends to more general types of measurements including time-varying
convolution with a compactly supported kernel