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arXiv · 1001.2952

On the complexity of Mumford-Shah type regularization, viewed as a relaxed sparsity constraint

Boris Alexeev·Rachel Ward
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Abstract

We show that inverse problems with a truncated quadratic regularization are NP-hard in general to solve, or even approximate up to an additive error. This stands in contrast to the case corresponding to a finite-dimensional approximation to the Mumford-Shah functional, where the operator involved is the identity and for which polynomial-time solutions are known. Consequently, we confirm the infeasibility of any natural extension of the Mumford-Shah functional to general inverse problems. A connection between truncated quadratic minimization and sparsity-constrained minimization is also discussed.

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Boris Alexeev, Rachel Ward. 2010-01-18. On the complexity of Mumford-Shah type regularization, viewed as a relaxed sparsity constraint. https://doi.org/10.1109/tip.2010.2048969

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