Error reconstruction surfaces of non stationary Gaussian fields

The statistical description of an optimal sampling reconstruction procedure (SRP) of non stationary Gaussian fields is given on the basis of the conditional mean rule. The non stationarity of field is determined in space, along of one axis, but not in time. A new type of the spatial covariance function of non stationary Gaussian field is suggested. A non trivial example of SRP of non stationary Gaussian field is given. The number of samples and their locations are arbitrary. We give precise calculations of the minimum mean square error reconstruction surfaces for the non stationary and stationary fields.