Quantitative Error Analysis for the Reconstruction of Derivatives

Laurent Condat (1) , Torsten Möller (2)

1 Equipe Image - Laboratoire GREYC - UMR6072
2 School of Computing Science

We present a general Fourier-based method which provides an accurate prediction of the approximation error, when the derivative of a signal s(t) is continuously reconstructed from uniform point samples or generalized measurements on s. This formalism applies to a wide class of convolution-based techniques. It provides a key tool, the frequency error kernel, for designing computationally efficient reconstruction schemes which are near optimal in the least-squares sense.

Mots clés: derivatives; reconstruction; sampling; interpolation; approximation; error analysis; frequency error kernel

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Laurent Condat, Torsten Möller. Quantitative Error Analysis for the Reconstruction of Derivatives. IEEE Transactions on Signal Processing, 2011, 59 (6), pp. 2965 - 2969. ⟨10.1109/TSP.2011.2119316⟩. ⟨hal-00462203v2⟩