| Abstract: | This article presents a model-based thin-plate smoothing method for optimal signal extraction and interpolation of missing data in spatial datasets. The method is based on a spectral EM algorithm where the two steps can be carried out in the frequency domain. In essence, the approach allows both dimensions to be treated separately from each other effectively rendering a likelihood that is easy to evaluate. As a result the algorithm is computationally inexpensive, in terms of both memory size and computing time, while allowing us to obtain an analytic expression for the asymptotic variance of the signal-to-noise ratio with which to construct confidence intervals of the missing data. Some numerical Monte Carlo simulations and a real data example using remotely sensed global aerosol optical thickness data illustrate the results given. Supplemental materials (Matlab computer code and dataset) are available online. |
