ISSN:
1573-7683
Keywords:
WMMR filters
;
LMS regression
;
Haar basis
;
piecewise constant signals
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract WMMR m filters weight the m ordered values in the window with minimum range. If m is not specified, it is assumed to be N + 1 for a window of length 2N + 1. Previous work has demonstrated a subclass of these filters that may be optimized for edge enhancement in that their output converges to the closest perfect edge. In this work it is shown that normalized WMMR m filters, whose weights sum to unity, are affine equivariant. The concept of the breakpoint of a filter is discussed, and the optimality of median and WMMR filters under the breakpoint concept is demonstrated. The optimality of a WMMR m filter and of a similar generalized-order-statistic (GOS) filter is demonstrated for various non-L Pcriterion, which we call closeness measures. Fixed-point results similar to those derived by Gallagher and Wise (see N.C. Gallagher and G.L. Wise, IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-29, 1981, pp. 1136–1141) for the median filter are derived for order-statistic (OS) and WMMR filters with convex weights (weights that sum to anity and are nonnegative), i.e., we completely classify the fixed points under the assumption of a finite-length signal with constant boundaries. These fixed points are shown to be almost always the class of piecewise-constant (PICO) signals. The use of WMMR filters for signal decomposition and filtering based on the Haar basis is discussed. WMMR filters with window width 2N + 1 are shown to be linear over the PICO(N + 1) signals (minimum constant length N+1). Concepts similar to lowpass, highpass, and bandpass for filtering PICO signals are introduced. Application of the filters to 1-dimensional biological data (non-PICO) and images of printed-circuit boards is then demonstrated, as is application to images in general.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00118584
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