Technical Program

Paper Detail

Paper:SS-8.6
Session:Innovations in Sampling Theory and Applications
Time:Thursday, May 20, 14:40 - 15:00
Presentation: Special Session Lecture
Topic: Special Sessions: Innovations in Sampling Theory and Applications
Title: QUANTITATIVE L^2 APPROXIMATION ERROR OF A PROBABILITY DENSITY ESTIMATE GIVEN BY IT SAMPLES
Authors: Thierry Blu; Swiss Federal Institute of Technology (EPFL) 
 Michael Unser; Swiss Federal Institute of Technology (EPFL) 
Abstract: We present a new result characterized by an exact integral expression for the approximation error between a probability density and an integer shift invariant estimate obtained from its samples. Unlike the Parzen window estimate, this estimate avoids recomputing the complete probability density for each new sample: only a few coefficients are required making it practical for real-time applications. We also show how to obtain the exact asymptotic behavior of the approximation error when the number of samples increases and provide the trade-off between the number of samples and the sampling step size.
 
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