New insights into one-norm solvers from the Pareto curve [pdf 296K] Gilles Hennenfent and Ewout van den Berg and Michael P. Friedlander and Felix J. Herrmann Geophysical inverse problems typically involve a trade off between
data misfit and some prior. Pareto curves trace the optimal trade
off between these two competing aims. These curves are commonly used
in problems with two-norm priors where they are plotted on a log-log
scale and are known as L-curves. For other priors, such as the
sparsity-promoting one norm, Pareto curves remain relatively
unexplored. We show how these curves lead to new insights in
one-norm regularization. First, we confirm the theoretical
properties of smoothness and convexity of these curves from a
stylized and a geophysical example. Second, we exploit these crucial
properties to approximate the Pareto curve for a large-scale
problem. Third, we show how Pareto curves provide an objective
criterion to gauge how different one-norm solvers advance towards
the solution.
Miscellaneous
User's manual for SLIM programs in Madagascar [pdf 376K] Gilles Hennenfent This guide documents the contributions to Madagascar made by authors
from the Seismic Laboratory for Imaging and Modeling
(SLIM) at the University of British
Columbia (UBC).
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