Local Sampling and Reconstruction in Spline Signal Spaces and Multiply Generated Spline Signal Spaces

The local reconstruction from samples is one of most desirable properties for many applications in signal processing. Local sampling is practically useful since we need only to consider a signal on a bounded interval and computer can only process only finite samples. However, the local sampling and reconstruction problem has not been given as much attention. Most of known results concern global sampling and reconstruction. In this paper, we give local sampling and reconstruction in special shift-invariant spaces, spline subspaces and multiply generated spline subspaces. Some known results are generalized by our results.