A wavelet- or lifting-scheme-based imputation method

The paper proposes a new approach to imputation using the expected sparse representation of a surface in a wavelet or lifting scheme basis. Our method incorporates a Bayesian mixture prior for these wavelet coefficients into a Gibbs sampler to generate a complete posterior distribution for the variable of interest. Intuitively, the estimator operates by borrowing strength from those observed neighbouring values to impute at the unobserved sites. We demonstrate the strong performance of our estimator in both one- and two-dimensional imputation problems where we also compare its application with the standard imputation techniques of kriging and thin plate splines.