Conference Proceeding

Towards a general theory of robust nonlinear filtering: selection filters

Dept. of Electr. Eng., Delaware Univ., Newark, DE
Acoustics, Speech, and Signal Processing, 1988. ICASSP-88., 1988 International Conference on (impact factor: 4.63). 05/1997; DOI:10.1109/ICASSP.1997.604721 ISBN: 0-8186-7919-0 pp.3837 - 3840 vol.5 In proceeding of: Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference on, Volume: 5
Source: IEEE Xplore

ABSTRACT In this paper we introduce a general framework for edge preserving
filters, derived from the powerful class of M-estimators. First, we show
that under very general assumptions, any location estimator generates an
edge preserving filter if we approximate the estimate by one of the
input samples. Based on this premise, we propose the family of
S-estimators or S-filters, as a selection-type class of filters arising
from a computationally tractable “selectification” of
location M-estimators. S-filters inherit the richness of the theory
underlying the M-estimators framework, providing a very flexible family
of robust estimators with edge preservation capabilities. Several
properties of S-filters are studied. Sufficient and necessary conditions
are given for an S-filter to present edge enhancing capabilities, and
several novel filters within this framework are introduced and
illustrated. Data, figures and source code utilized in this paper are
available at http://www.ee.udel.edu/signals/robust/

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Keywords

computationally tractable “selectification”
 
figures
 
flexible family
 
general assumptions
 
input samples
 
location estimator
 
location M-estimators
 
M-estimators
 
M-estimators framework
 
necessary conditions
 
novel filters
 
powerful class
 
present edge
 
richness
 
robust estimators
 
S-estimators
 
S-filters
 
selection-type class
 
source code utilized
 
Sufficient
 

J.G. Gonzalez