We study the blind deconvolution problem in the case where the input noise has a finite discrete support and the transfer linear system is not necessarily minimum phase. We propose a new family of estimators built using algebraic considerations. The estimates are consistent under very wide assumptions: The input signal need not be independently distributed; the cardinality of the finite support may be estimated simultaneously. We consider in particular AR systems: In this case, we prove that the estimator of the parameters is perfect a.s. with a finite number of observations.
Publié le : 1996-10-14
Classification:
Deconvolution,
contrast function,
$T$-system,
discrete linear systems,
62G05,
62M09,
62M10
@article{1069362305,
author = {Gamboa, F. and Gassiat, E.},
title = {Blind deconvolution of discrete linear systems},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 1964-1981},
language = {en},
url = {http://dml.mathdoc.fr/item/1069362305}
}
Gamboa, F.; Gassiat, E. Blind deconvolution of discrete linear systems. Ann. Statist., Tome 24 (1996) no. 6, pp. 1964-1981. http://gdmltest.u-ga.fr/item/1069362305/