Title :
Quantitative Error Analysis for the Reconstruction of Derivatives
Author :
Condat, Laurent ; Möller, Torsten
Author_Institution :
GREYC Lab., CNRS-UCBN-ENSICAEN, Caen, France
fDate :
6/1/2011 12:00:00 AM
Abstract :
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.
Keywords :
convolution; error analysis; signal reconstruction; Fourier-based method; approximation error; computationally efficient reconstruction scheme; convolution-based technique; derivative reconstruction; frequency error kernel; quantitative error analysis; Image reconstruction; Interpolation; Kernel; Reconstruction algorithms; Signal processing; Spline; Approximation; derivatives; error analysis; frequency error kernel; interpolation; reconstruction; sampling;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2011.2119316