have been tuned experimentally, Figure 1 shows an
example of PSNR and MSSIM values obtained sev
eral values of p. It is shown that both measures give
the similar optimum values of p. For example, with
α =1.5 the optimum value of p is around 1.3, and
with α =1.9 the optimum value of p is around 1.7.
We show in Figure 2 the results of the adaptive l
p

norm ﬁlter in suppressing impulsive noise in Lena im
age. Figure 2(a) shows the image corrupted by im
pulsive noise which is represented by Symmetrical α
stable noise (α=0.5). The output of the NLMS ﬁlter
is shown is Figure 2(b). Figure 2(c) shows the ﬁltered
image by using the weighted median ﬁlter (WMF).
The ﬁltered image using the weighted myriad ﬁlter
(WMyF) is shown in Figure 2(d). Figure 2(e) shows
the ﬁltered image using the 2D adaptive LMP ﬁlter
with ﬁxed stepsize. Finally, the ﬁltered image by the
normalized l
p
norm ﬁlter is shown in Figure 2(f). The
ﬁlter parameters have been tuned to obtain the best vi
sual results.
The visual quality demonstrates the superiority of
using fractional lowerorder statistics ﬁltering algo
rithms which gives a good performance with edges
and ﬁne image details preserving.
Table 1 summarizes respectively the FSNR and
the MSSIM achieved by the adaptive proposed ﬁl
ters with different values of α . According to
these results, the ﬁltered image using l
p
norm ﬁl
ter has higher FSNR and MSSIM improvement from
the LMP/NLMP linear equalizers than those of the
NLMS ﬁlter, weighted median ﬁlter and weighted
myriad ﬁlter. The measures achieved by the normal
ized l
p
norm ﬁlter give good improvement in term of
visual quality and signaltonoise ratio improvement.
When a reference image is not available. We use
the same methodology as described in (Kotropoulos
and Pitas, 2001). We have tested the robustness of
the ﬁlter coefﬁcients that are determined at the end
of a training session and are applied to ﬁlter a noisy
image that has been produced by corrupting a differ
ent reference image than the one used in the training
session. In Figure 3, we present a ﬁltered house im
age using the coefﬁcients determined at the end of a
training session on lenna image. The same noise pa
rameters have been used during the training session.
When, regarding the quality of the ﬁltered images and
the quality evaluation measures, we can say that the
proposed ﬁlter is very good for αstable noise perfor
mance measurement.
5 CONCLUSION
In this paper, we presented a 2D adaptive l
p
norm
ﬁlter for noise suppression in images. Experimental
results on natural images showed marked improve
ment in visual and numerical qualities when using the
normalized l
p
norm algorithm adaptation. The ﬁlter
is very suitable for αstable and impulsive noise re
moval.
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