figure 9. the noise-to-noise criterion. from left to right and from top to bottom: original noise image of standard deviation 20, Gaussian
convolution, anisotropic filtering, total variation, neighborhood filter, translation invariant wavelet thresholding, DCt sliding window Wiener
filter, and nL-means. Parameters have been fixed for each method so that the noise standard deviation is reduced by a factor 4.
table 1. mean square error table.
Image s Gf af tV Ynf DCt Wav.thresh nL-means
Boat 8 53 38 39 39 33 28 23
lena 20 120 114 110 129 105 81 68
Barbara 25 220 216 186 176 111 135 72
Baboon 35 507 418 365 381 396 365 292
Wall 35 580 660 721 598 325 712 59
A smaller mean square error indicates that the estimate is closer to the original image. The numbers have to be compared on
each row. The square of the number on the left-hand column gives the real variance of the noise. By comparing this square to
the values on the same row, it is quickly checked that all studied algorithms indeed perform some denoising. This is a sanity
check! In general, the comparison performance corroborates the previously mentioned quality criteria.
The algorithm favors pixels with a similar local configuration, as the similar configurations move, so do the weights.
Thus, the algorithm is able to follow the similar configurations when they move without any explicit motion computation (see Figure 10). This is not the case of classical movie
denoising algorithms, which are motion compensated (see
Buades et al. 9 for more details on this discussion). The very
same idea on movie denoising can be applied for
super-resolution, an image zooming method by which several frames
from a video, or several low resolution photographs, can be
fused into a larger image. 20, 37
Improvements or adaptations of the NL-means algorithm have been proposed for the denoising of several
types of data: in fluorescence microscopy, 5 cryon microscopy, 15 magnetic resonance imaging (MRI), 31 and 3D data
set points. 47
Most successful improvement of NL-means combine
the nonlocal principle with former classic algorithms and
have indeed shown an improved denoising performance.
Probably the best performing methods so far are the hybrid
method BM3D proposed in Dabov et al. 14 and the NL-PCA
proposed in Zhang et al. 48 Both algorithms combine not
less than block-matching, a linear transform thresholding,
and Wiener filtering.