Irregular sampling theorems for wavelet subspaces

TL;DR: An algorithm is presented which can relax the upper bound for sampling in some wavelet subspaces by using scaling functions and which can estimate a proper upper bound of sup/sub /spl kappa//|/spl delta//sub / spl kappa| such that the irregularly sampled signals can be recovered.

Abstract: From the Paley-Wiener 1/4-theorem, the finite energy signal f(t) can be reconstructed from its irregularly sampled values f(k+/spl delta//sub /spl kappa//) if f(t) is band-limited and sup/sub /spl kappa//|/spl delta//sub /spl kappa//|<1/4. We consider the signals in wavelet subspaces and wish to recover the signals from its irregular samples by using scaling functions. Then the method of estimating the upper bound of sup/sub /spl kappa//|/spl delta//sub /spl kappa//| such that the irregularly sampled signals can be recovered is very important. Following the work done by Liu and Walter (see J. Fourier Anal. Appl., vol.2, no.2, p.181-9, 1995), we present an algorithm which can estimate a proper upper bound of sup/sub /spl kappa//|/spl delta//sub /spl kappa//|. Compared to Paley-Wiener 1/4-theorem, this theorem can relax the upper bound for sampling in some wavelet subspaces.