| 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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