Irregular Sampling Theorems for Wavelet Subspaces - Information Theory, IEEE Transactions on

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