


 Fast logdecon with a quasiNewton 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 logdecon method
corresponds to the crosscorrelation of the residual (the reflectivity series)
with the softclipped residual (see Claerbout et al. (2012) for
a generalization with a variable gain). The pseudocode below
shows the steepest descent algorithm.
Once
is estimated, we obtain the wavelet
and the sparse
decon output
, where
is the Fourier transformed
input data.
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