  We present a new technique for the interpolation of discretely-sampled
non-negat ive scalar fields across regions of missing data. Any set of basis
functions can be used, though the method is fastest when they are close to
orthogonal. We sho w how the technique may be efficiently applied when the
discrete sampling rate v aries across the field. Regularisation is desirable to
avoid over-fitting noisy data, and is necessary when the regions of missing
data are larger than the requ ired resolution. We present and investigate
methods for such regularisation.
