Ak. Dey et al., INPUT RECOVERY FROM NOISY OUTPUT DATA, USING REGULARIZED INVERSION OFTHE LAPLACE TRANSFORM, IEEE transactions on information theory, 44(3), 1998, pp. 1125-1130
Citations number
17
Categorie Soggetti
Computer Science Information Systems","Engineering, Eletrical & Electronic","Computer Science Information Systems
wIn a dynamical system the input is to be recovered from finitely many
measurements, blurred by random error, of the output of the system. A
s usual, the differential equation describing the system is reduced to
multiplication with a polynomial after applying the Laplace transform
. It appears that there exists a natural, unbiased, estimator for the
Laplace transform of the output, from which an estimator of the input
can be obtained by multiplication with the polynomial and subsequent a
pplication of a regularized inverse of the Laplace transform. It is po
ssible, moreover, to balance the effect of this inverse so that ill-po
sedness remains restricted to its actual source: differentiation. The
rate of convergence of the integrated mean-square error is a positive
power of the number of data. The order of the differential equation ha
s an adverse effect on the rate which, on the other hand, increases wi
th the smoothness of the input as usual.