Raster Extrapolation

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I would like to know, if QGIS (or different software) has a method, how to extrapolate raster values to larger area (outer boundary).

I have a boundary(.shp), which is 40 m far from the edge of raster. I want to fill the space between raster edge and polygon boundary with values extrapolated from edges of raster. Some cubic spline method would be ideal.



Can anyone help, please?



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