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{\large Hui Huang \\
{\bf Optimal Estimation for Signal Priors}}

University of British Columbia \\ 201-2366 Main Mall \\ Vancouver \\ BC V6T1Z4 Canada
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{\tt hhuang@eos.ubc.ca}\\
Eldad Haber\end{center}

We consider the problem of estimating signal priors, which are used in
the $\ell_1$-regularization and the resulting inverse problem has a
stabilized solution. From a Bayesian viewpoint, we first define a
multivariate $\ell_1$-Laplace density function
and then solve a maximum likelihood problem with an added
$\ell_1$-norm penalty term. The problem as formulated is convex but
the memory requirements and the nonlinear non-smooth sub-gradient
equations are prohibitive for large-scale problems. We develop an
iterative algorithm to efficiently solve such large problems and
demonstrate the selected priors generally behave better than those
commonly used ones in the signal processing.


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