The Annals of Statistics

Outlier robust corner-preserving methods for reconstructing noisy images

Martin Hillebrand and Christine H. Müller

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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.

Article information

Ann. Statist., Volume 35, Number 1 (2007), 132-165.

First available in Project Euclid: 6 June 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties 62G35: Robustness

Nonparametric regression M-estimation corner-preserving M-kernel estimation robustness consistency outliers


Hillebrand, Martin; Müller, Christine H. Outlier robust corner-preserving methods for reconstructing noisy images. Ann. Statist. 35 (2007), no. 1, 132--165. doi:10.1214/009053606000001109.

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