![](bg6.png)
tures, and original contrasts are visually well recov-
ered with no undesirable artifacts (PSNR= 32.68db
for ”Lena”). To better appreciate the accuracy of the
restoration process, the square of the difference be-
tween the original image and the recovered image is
shown in Figure 2(d), where the dark values corre-
spond to a high-confidence estimate. As expected,
pixels with a low level of confidence are located in
the neighborhood of image discontinuities. For com-
parison, we show the image denoised by Non-Local
Means Filter in Figures 2(e),(f). The overall visual
impression and the numerical results are improvedus-
ing our algorithm.
The Optimal Weights Filter seems to provide a
feasible and rational method to detect automatically
the details of images and take the proper weights for
every possible geometric configuration of the image.
The distribution of the weights inside the search win-
dow U
x
0
,h
depends on the estimated brightness vari-
ation function
b
ρ
K,x
0
(x), x ∈ U
x
0
,h
. If the estimated
brightness variation
b
ρ
K,x
0
(x) is less than ba (see Theo-
rem 1), the similarity between patches is measured by
a linear decreasing function of
b
ρ
K,x
0
(x); otherwise it
is zero. Thus ba acts as an automatic threshold.
4 CONCLUSIONS
We have proposed a new filter to remove Gaus-
sian noise, based on optimization of weights in the
weighted means approach. Our analysis shows that
a triangular kernel is preferred rather then the Gaus-
sian kernel. The proposed filter improves the usual
Non-Local Means Filter both numerically and visu-
ally in denoising performance; it also has the advan-
tage to be adaptive in the sense that it calculates au-
tomatically the good bandwidth of the triangular ker-
nel (while in the Non-Local Means Filter the choice
of the bandwidth parameter in the Gaussian kernel is
delicate). We hope that the optimal weights that we
deduced can also bring similar improvements for re-
cently developed algorithms where the basic idea of
the Non-Local means filter is used.
ACKNOWLEDGEMENTS
The authors are grateful to the reviewers for helpful
comments and remarks. The work has been partially
supported by the National Natural Science Founda-
tion of China, Grant No. 11101039 and Grant No.
11171044.
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