Sampling and quasi-optimal approximation for signals in a reproducing kernel space of homogeneous type

This paper considers the reconstruction of signals in a reproducing kernel space of homogeneous type from finite samples. First, a pre-reconstruction operator based on finite samples and probability measure is proposed and its bounded property is studied. Secondly, the stability and an iterative algorithm with exponential convergence are established for sampling and recovering signals in a subspace of homogeneous reproducing kernel space. Then, we show that the proposed algorithm also provides a quasi-optimal approximation to signals in a reproducing kernel space of homogeneous type. Finally, some numerical simulations are given to reconstruct signals on an interval.