Learning Iterative Image Reconstruction - Hierarchical Neural Networks for Image Interpretation - page 187

(a)
(b)
Fig. 9.17. Some examples from the MNIST dataset: (a) original images; (b) degraded with
reduced contrast, random background level, noise, and saturation.
the choice of the wavelet transformation is usually fixed, and that the thresholding
ignores dependencies between neighboring locations within a scale and between
scales.
Yang et al. [246] demonstrated that a linear auto-associator can be used for de-
noising faces if a wavelet representation is used. The output of the system has a high
perceptual quality if the noise level is moderate. However, since the system is linear,
no hard decisions can be made, and the network's output resembles overlayed faces
if the noise level is high. Hence, the need for non-linear behavior becomes obvious.
9.4.1 Image Degradation
In the next experiment, it is demonstrated that the same method, which was use-
ful for filling-in occluded parts, can be applied to noise removal as well. The same
network architecture and the same MNIST digits are used to simultaneously learn
noise removal and contrast enhancement. The only difference is the image degrada-
tion procedure.
To degrade the images, the pixel intensities are scaled from the interval [0 , 1] to
the range [0 . 25 , 0 . 75] . This reduces image contrast. To simulate variance in light-
ing and paper brightness, a random background level is added that is uniformly
distributed in the range [ − 0 . 25 , 0 . 25] . Additive uniform pixel noise, drawn from
[ − 0 . 25 , 0 . 25] , simulates sensor noise. Finally, the pixel intensities are clipped at
zero and one to resemble sensor saturation. Figure 9.17 shows some digits from the
MNIST dataset that have been degraded in this way.
The network was trained to reconstruct the original images on a working set of
increasing size for twelve time steps using BPTT and RPROP. A low-activity prior
was used to encourage the development of sparse representations.
9.4.2 Experimental Results
Figure 9.18 illustrates the reconstruction process of the trained network for a test
example. The activity of the entire network is shown over time. One can observe
that all features contribute to the computation. In the first time steps, the confidence
of the digit's lines visible in the bottom layer is not very high since locally they look
similar to some background structures. The confidence increases as more context
influences the result. Finally, background clutter is removed from the output feature
array, and the lines are amplified.