Computation of wavelet coefficients from average samples

There exist efficient methods to compute the wavelet coefficients of a function f(t)f(t) from its point samples f(T[n+τ])f(T[n+τ]), n∈Nn∈N. However, in many applications the available samples are average samples of the type ∫−∞∞f(T[t+n+τ])u(t)dt, where the averaging function u(t)u(t) reflects the characteristic of the acquisition device. In this work, methods to compute the coefficients in a biorthogonal wavelet system from average samples are studied. Error estimations are obtained and using them, the optimal values for the parameters in the proposed approximation rules are calculated. The obtained error estimations can also be applied to the rules that compute the coefficients from point samples, and thus, these estimations can be used to compare and to choose between the different methods proposed in the literature. The methods proposed here also allow us to compute the biorthogonal wavelet coefficients from the coefficients in another biorthogonal wavelet system.