Fuzzy Methods in Nonlinear Signal Processing: Part II—Applications - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 70

The focus of this chapter is the application of the developed filters to a
wide array of signal processing and communications problems. Indeed, be-
cause the affinity and fuzzy concepts are easily embedded in existing meth-
ods, nearly all problems can be successfully addressed through affinity- or
fuzzy-based methods. To give an appreciation of the performance gains that
can be achieved through more general methods, results are presented for
fuzzy theory-based filters applied to the problems of robust frequency se-
lective filtering, Synthetic Aperture Radar image filtering, time-frequency
domain filtering, multiresolution signal representations, surface smoothing,
image smoothing, zooming, and deblocking, and multiuser detection. In each
case, we compare the performance of the fuzzy generalizations to their crisp
counterparts as well as other methods reported in the literature designed to
address the problem at hand. The presented results show that the fuzzy gener-
alizations yield improved performance over existing methods. These results,
coupled with the wide applicability of the fuzzy methods, indicate that fuzzy
SR ordering and the resulting filter generalizations constitute important tools
for modern signal processing applications.
This chapter is organized as follows. Applications of affine filters are cov-
ered in Section 3.2. There, the median affine filter is applied to the problems
of robust frequency-selective filtering and signal multiresolution representa-
tions. Also in this section, the center affine filter is applied to the problems
of inverse Synthetic Aperture Radar and time-frequency domain filtering,
as well as image deblocking. Section 3.3 covers problems best addressed by
fuzzy ordering and fuzzy weighted median filtering methods. Specifically,
fuzzy weighted median type methods are applied to the problems of image
(gray scale and color) and surface smoothing, image zooming, and noisy im-
age sharpening. Also, the fuzzy ranks are used to address the problem of
multiuser detection. Last, conclusions are drawn in Section 3.4.

3.2 Affine Filter Applications

Affine filters have a broad spectrum of potential applications due to their
wide range of filter characteristics and their flexibility. The different structures
that the filters can take on lend themselves to different problems. The first
problem considered is robust frequency selective filtering, in which temporal
(spatial) order of samples must be exploited to gain frequency selectivity,
while some rank ordering should be considered to ensure robust behavior.
This problem is effectively addressed through median affine filtering. These
same characteristics allow median affine filters to be effectively employed in
multiresolution signal decomposition problems, which are considered next.
The following three problems focus on cases where the central observation
sample plays a crucial role, and are thus effectively addressed through center