Oversampling in wavelet subspaces

Recently, several extensions of classical Shannon sampling theory to wavelet subspaces have been reported. This paper is devoted to uniform and periodic nonuniform oversampling in wavelet subspaces. Specifically, we provide a stability analysis and we introduce a technique for calculating the condition number of wavelet subspace sampling operators. It is shown that oversampling results in improved numerical stability. We consider the reconstruction from noisy samples and we characterize compactly supported scaling functions having compactly supported synthesis functions. Finally, it is shown that in the oversampled case the synthesis functions are not uniquely determined