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Statistical Optimality of Hermite Splines for the Reconstruction of Self-Similar Signals

V. Uhlmann

SIAM Conference on Imaging Science (SIS'18), Bologna, Italian Republic, June 5-8, 2018, session MS47-2.



Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation. Assuming a suitable statistical model, we demonstrate that this method is optimal for reconstructing random signals in Papoulis' generalized sampling framework. More precisely, we show the equivalence between cubic Hermite interpolation and the linear minimum mean-square error (LMMSE) estimation of a second-order Lévy process.


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