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 gradient. 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


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