Interpolation of Discretely-Sampled Density Fields
  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. 
Will Saunders and Bill E. Ballinger