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.
"Blind deconvolution of discrete linear systems." Ann. Statist. 24 (5) 1964 - 1981, October 1996. https://doi.org/10.1214/aos/1069362305