||Fast log-decon with a quasi-Newton solver||
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The steepest descent method requires the computation of the gradient.
The model space is a vector of filter coefficients
Claerbout shows that the gradient
of the sparse log-decon method
corresponds to the crosscorrelation of the residual (the reflectivity series)
with the soft-clipped residual (see Claerbout et al. (2012) for
a generalization with a variable gain). The pseudo-code below
shows the steepest descent algorithm.
is estimated, we obtain the wavelet
and the sparse
is the Fourier transformed