Marc Raimondo - CMI
Marc Raimondo - CMI
Marc Raimondo - CMI
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The Annals of Statistics<br />
2004, Vol. 32, No. 5, 1781–1804<br />
DOI 10.1214/009053604000000391<br />
© Institute of Mathematical Statistics, 2004<br />
PERIODIC BOXCAR DECONVOLUTION AND DIOPHANTINE<br />
APPROXIMATION<br />
BY IAIN M. JOHNSTONE 1 AND MARC RAIMONDO 2<br />
Stanford University and University of Sydney<br />
We consider the nonparametric estimation of a periodic function that is<br />
observed in additive Gaussian white noise after convolution with a “boxcar,”<br />
the indicator function of an interval. This is an idealized model for the<br />
problem of recovery of noisy signals and images observed with “motion<br />
blur.” If the length of the boxcar is rational, then certain frequencies are<br />
irretreviably lost in the periodic model. We consider the rate of convergence<br />
of estimators when the length of the boxcar is irrational, using classical<br />
results on approximation of irrationals by continued fractions. A basic<br />
question of interest is whether the minimax rate of convergence is slower<br />
Luminy 12/08 – p.3
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