Estimation of Residual Wavelets
, by Clement Kostov and Fabio Rocca
A solution is presented for the blind deconvolution problem, where
the wavelet is estimated from the convolved output data and
from statistical assumptions on the input process and the wavelet.
The key steps in this method are the computation of the gradient
of a likelihood function, and of the gain operator applied to that
The case of independent identically distributed (iid) input data samples,
drawn from generalized Gaussian distributions, is presented in detail.
Expressions for the variance of the estimators are derived as a
function of the distribution of the input process, of the number
of input data points and of the prior information on the wavelet type.
Numerical simulations show also the dependence of the variance on
the norm of the wavelet.
Despite a very distinct derivation, the method presented in this
paper shows interesting similarities with minimum entropy deconvolution
(MED) methods. The form of the estimators and the results on their
variances are compared for both methods.SEP Computer Update