I am working on gap filling techniques for satellite remote-sensing data. Due to the cloud cover of the study area, nearest neighbors might not be a good option. Anybody works in this area that might want to share their experience. e.g methods, software.
The key to the question here is 'temporal'. Spatial gap filling has been explored exhaustively for the purposes of gap filling Landsat 7 SLC off data, and there are plenty of published approaches worth checking out. Combining spatial and temporal imagery to gap fill introduces more opportunities for finding the 'right' pixel but opens up the challenge of introducing a lot more selection criteria for selecting the 'right' pixel to fill the gap. Choosing a pixel that is at the same location and proximal (close) in time makes more sense than choosing a spatially neighbouring pixel because you're actually filling the raster with a real observation... the trick is of course that you've got to define how close in time is acceptable to select from (select from a scene that's from a different season and you'll end up with pop-corn artefacts where your clouds are). Only a decent understanding of the local phenology/seasonality will allow you to determine how 'close' in time a pixel needs to be before its a suitable candidate for compositing. Once you've got that sorted, grab a temporal stack of images, co-register them, fire up GDAL and python and away you go :)
The excellent work of Markus Neteler, 2010. Estimating daily land surface temperatures in mountainous environments by reconstructed MODIS LST data, Remote Sensing, 2:1, 333-351 (http://goo.gl/3znPN) could be the perfect starting point for your research.
I found very useful the book from Cressie N. and Wikle C.K., Statistics for Spatio-Temporal Data, Wiley 2011 where you find spatio-temporal statistics widely and deeply explained.
A first question is whether you are going to interpolate to missing spatial data locations or to missing time locations (or possibly both). The various forms of kriging are just the same for spatial temporal data as for spatial data, i,e, the equations are the same. However the problem of fitting a spatial temporal variogram or covariance function is quite different. There are several different and non-overlapping classes of valid models in the literature, e.g. Gneiting, Myers-De Iaco-Posa. There are also some software packages, see Computers & Geosciences. The latest version of the R package gstat uses an invalid model, i.e. the product of a spatial variogram and a temporal variograms (the product of two variograms is not a variogram)
@Donald Myers: right: the spatial dimension and the temporal dimensions are not always separable. I understood that studying Cressie&Wikle "Statistics for Spatio-temporal Data" (Wiley) that I suggest to everyone doing spatio-temporal analysis.
Both the Gneiting and the product-sum model of De Iaco et al are non-separable although the product sum model includes a separable model as a special case. The Fourier transform model of Cressie-Huang is a special case of an integrated product sum model
It's never too late to give an answer.
I'm working on this problem using mainly stochastic filters, you can check my work and references therein.
Conference Paper Spatio-temporal interpolation of Sea Surface Temperature usi...
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