Locally monotone robust approximation of sequences

The study of nonlinear smoothers for the removal of impulsive noise in a sequence leads to the problem of the unique and stable allocation of a particular root to a given noise-corrupted sequence. An established procedure is iteration of a median smoother till convergence. This process is neither we...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 36; no. 3; pp. 399 - 408
Main Authors Rohwer, C.H., Toerien, L.M.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 24.09.1991
Elsevier
Subjects
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
idempotent
impulsive noise
medians
Nonlinear
roots
smoothers
Theoretical computing
idempotent
Nonlinear
impulsive noise
medians
roots
smoothers
Signal processing
Median
Filtering
Image processing
Smoothing
Applied mathematics
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Summary:The study of nonlinear smoothers for the removal of impulsive noise in a sequence leads to the problem of the unique and stable allocation of a particular root to a given noise-corrupted sequence. An established procedure is iteration of a median smoother till convergence. This process is neither well defined, nor well posed. Recursive smoothing, used to circumvent these intuitively perceived problems, is not satisfactory either. Simple equivalent smoothing operators exist that the allocate a class of sequences that are roots of the median smoother, as well as a whole collection of equivalent smoothers. This class is an interval in the usual lattice on sequences. The allocation is well defined and well posed, and blends into the framework of interval arithmetic.
ISSN:0377-0427
1879-1778
DOI:10.1016/0377-0427(91)90019-G