Open Access
February 2007 Outlier robust corner-preserving methods for reconstructing noisy images
Martin Hillebrand, Christine H. Müller
Ann. Statist. 35(1): 132-165 (February 2007). DOI: 10.1214/009053606000001109


The ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother. Unfortunately, they usually seem to be at odds with each other; one can only improve one property at the cost of the other. By combining M-smoothing and least-squares-trimming, the TM-smoother is introduced as a means to unify corner-preserving properties and outlier robustness. To identify edge- and corner-preserving properties, a new theory based on differential geometry is developed. Further, robustness concepts are transferred to image processing. In two examples, the TM-smoother outperforms other corner-preserving smoothers. A software package containing both the TM- and the M-smoother can be downloaded from the Internet.


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Martin Hillebrand. Christine H. Müller. "Outlier robust corner-preserving methods for reconstructing noisy images." Ann. Statist. 35 (1) 132 - 165, February 2007.


Published: February 2007
First available in Project Euclid: 6 June 2007

zbMATH: 1114.62050
MathSciNet: MR2332272
Digital Object Identifier: 10.1214/009053606000001109

Primary: 62G08
Secondary: 62G20 , 62G35

Keywords: consistency , corner-preserving , M-estimation , M-kernel estimation , Nonparametric regression , Outliers , robustness

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 1 • February 2007
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