Irregular sampling theorems for wavelet subspaces

From the Paley-Wiener 1/4-theorem, the finite energy signal f(t) can be reconstructed from its irregularly sampled values f(k + delta(k)) if f(t) is band-limited and sup(k) {delta(k)} < 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 way to estimate the upper bound of sup(k) \delta(k)\ such that the irregularly sampled signals can be recovered is very important. Following the work done by Liu and Waiter, we present an algorithm which can estimate a proper upper bound of sup(k) \delta(k)\. Compared to Paley-Wiener 1/4-theorem, this theorem can relax the upper bound fdr sampling in some wavelet subspaces.