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{1181100184,
author = {Hillebrand, Martin and M\"uller, Christine H.},
title = {Outlier robust corner-preserving methods for reconstructing noisy images},
journal = {Ann. Statist.},
volume = {35},
number = {1},
year = {2007},
pages = { 132-165},
language = {en},
url = {http://dml.mathdoc.fr/item/1181100184}
}
Hillebrand, Martin; Müller, Christine H. Outlier robust corner-preserving methods for reconstructing noisy images. Ann. Statist., Tome 35 (2007) no. 1, pp. 132-165. http://gdmltest.u-ga.fr/item/1181100184/