This paper describes an extension of the Minimum Sobolev Norm interpolation scheme to an approximation scheme. A fast implementation of the MSN interpolation method using the methods for Hierarchical Semiseparable (HSS) matrices is described and experimental results are provided. The approximation scheme is introduced along with a numerically stable solver. Several numerical results are provided comparing the interpolation scheme, the approximation scheme and Thin Plate Splines. A method to decompose images into smooth and rough components is presented. A metric that could be used to distinguish edges and textures in the rough component is also introduced. Suitable examples are provided for both the above.
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