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An Efficient Implementation of Hybrid $l^1/l^2$ Norm IRLS Method as a Robust Inversion  

Ji, Jun (Department of Information System Engineering, Hansung University)
Publication Information
Geophysics and Geophysical Exploration / v.10, no.2, 2007 , pp. 124-130 More about this Journal
Abstract
Least squares ($l^2$ norm) solutions of seismic inversion tend to be very sensitive to data points with large errors. The $l^1$ norm minimization gives more robust solutions, but usually with higher computational cost. Iteratively reweighted least squares (IRLS) method gives efficient approximate solutions of these $l^1$ norm problems. I propose an efficient implementation of the IRLS method for a hybrid $l^1/l^2$ minimization problem that behaves as $l^2$ norm fit for small residual and $l^1$ norm fit for large residuals. The proposed algorithm shows more robust characteristics to the decision of the threshold value than the l1 norm IRLS inversion does with respect to the threshold value to avoid singularity.
Keywords
IRLS; hybrid norm$l^1/l^2$ norm; robust inversion; velocity stack;
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