Irregular sampling theorems for wavelet subspaces

In this paper, we provide reconstruction formulae and establish the algorithm to estimate the deviation bound for irregularly sampled signals in orthogonal and biorthogonal wavelet subspaces respectively after introducing the function class L^λ_σ [a,b], that does not require the symmetricity constraints δ _k=-δ_-k of Paley-Wiener´s for sampling, but also relaxes its deviation bound in some wavelet subspaces. Then we obtain an irregular sampling theorem and an algorithm for general wavelet subspaces deduced from the biorthogonal case. Furthermore the theorems and algorithms are modified to a more useful case by using the Zak transform Z_φ(σ,ω) (Janssen, 1993)