Least-squares imaging and deconvolution using the hybrid norm conjugate-direction solver |

This solver is convenient to apply, because the function interface is almost the same as the traditional least-squares (L2) solver in the SEP library. The user must specify one additional parameter: the residual quantile. Fortunately this parameter has a clear physical meaning (Claerbout, 2009b). Users should assign this parameter according to prior observation or expectation of the model's spikiness/blockness.

In this paper we show the usefulness of the hybrid solver by applying it
on the LSI imaging and deconvolution problems. The *L*1 inversion of LSI imaging
(Least Squares Inverse) problem is preferable to L2 inversion, because
it better perseves the spikiness/sparseness that
are commonly encountered in reflectivity models. When the model
regularization is posed with the L2 norm, it is hard to honor
spikness/sparseness, because the L2 norm cannot
tolerate large values in the model. In contrast, the L1 type norm fits
our regularization goal very well.

A similar motivation applies to the deconvolution problem; conventional deconvolution assumes the reflectivity series to be random (white spectrum), whereas we argue that a sparse reflectivity series is more appropriate (and often more desirable) in practice.

Least-squares imaging and deconvolution using the hybrid norm conjugate-direction solver |

2010-05-19