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the results comparing the difference images I dif = I ref I denoised . In the review of denoising al-
gorithms in Ref. [ 19 ] the difference images were also used to compare denoising algorithms.
An ideal difference image would look like noise; if image structure comes through, image de-
tails are lost during denoising. Figure 2 (a) shows the difference of the reference image to the
image denoised by Zhang [ 4 ]: The image structure is clearly visible, which indicates that the
image was blurred. In Figure 2 (b) we observe finer image structures, thus finer details seem
to get lost. Additionally, the difference image is colored, which means that the error is an of-
set and thus the color of the denoised image does not correspond to the correct color of the
reference. The difference image in Figure 2 (c) shows the difference for the proposed Bayer
SA-DCT. The image is most similar to noise, thus it looks more random, which means that not
much image structure is lost and no color shift must be expected.
FIGURE 2 Difference to the reference for the test image “City” denoised using (a) the al-
gorithm of Zhang [ 4 ] , (b) Foi [ 6 ] , and (c) the proposed version of the SA-DCT.
Analyzing the results visually, we found that our method performs beter due to the low
spatial correlation of the error: the remaining denoising error appears less disturbing as it
is less correlated. We calculated the correlation coefficient between the denoising error—also
called “method noise”—at one pixel position and the denoising error at the neighboring pixel
positions. The spatial correlation is shown in Figure 3 (c). The data is shown for all three color
channels and for a 10 × 10 neighborhood. Additionally the numbers are given for the green
channel and a 3 × 3 neighborhood in Table 5 .
FIGURE 3 Spatial correlation of the difference images for red (left), green (middle), and blue
(right) channel. Displayed is the correlation for a 10 × 10 neighborhood. From top to bottom:
Foi [ 6 ] , Zhang [ 4 ] , and the proposed Bayer Data SA-DCT. Ideally only noise should be re-
moved from the image and thus the correlation of the difference image should be low.
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