Outlier robust corner-preserving methods for reconstructing noisy images

• 成果类型: Article
• 署名作者: Hillebrand, Martin; Mueller, Christine H.
• 署名单位: Technical University of Munich; Universitat Kassel
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001109
• 发表日期: 2007
• 页码: 132-165
• 关键词: estimators; smoothers

摘要

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 comer-preserving smoothers. A software package containing both the TM- and the M-smoother can be downloaded from the Internet.