On the Utility of Non-Negative Differentially Constrained Entropy-like Regularizors

Mathematics Research Report MRR95-045

On the Utility of Non-Negative Differentially Constrained Entropy-like Regularizors

Gerhard Landl and Robert S. Anderssen

Abstract: The utility of non-negative differentially constrained entropy-like regularizors is examined not only in terms of the standard stability, convergence and convergence rates, but also in terms of the important practical measures of asymptotics and shrinkage. In particular, it is shown that the unwanted shrinkage associated with the classical entropy regularizor $\int_\Omega p \log p dx$ does not, in general, hold for members of this class of entropy regularizors, the choice of which can be more specifically adapted to the problem context of the regularization than the classical entropy regularizor.

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