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such image-sequences are available. However, Baker and Kanade [12] have shown
that there exist fundamental limits on the reconstruction quality, even if infinitely
many low-resolution images are used. More specifically, since the constrained vol-
ume contains many solutions, a smoothness prior is usually used to select one of
them. This leads to overly smooth reconstructions.
One would like to have an intelligent method for expanding the resolution of
an image. It should keep edges sharp, which are implicitly described in the low-
resolution image, and it should make intelligent guesses about the details of textures.
A natural solution to this problem is to estimate the missing image details using the
non-uniform distribution of images. Since some image structures, such as edges
and lines, are more likely than others, a super-resolution method can be biased to
reconstruct them.
To make this approach work, a training set of aligned high-resolution and low-
resolution images is needed to estimate the prior. The more specific this training set
is, the sharper the prior will be. Three of such informed super-resolution methods
have been recently proposed.
Baker and Kanade describe in [12] a system that 'hallucinates' high-resolution
faces from low-resolution images. They use a database of normalized faces and find
from it the image patch most similar to the low-resolution input patch. To measure
similarity they use multiscale derivative features called parent structure vectors [34].
The method is also applied to images of text.
Freeman et al. [71] proposed example-based super-resolution as a simplified
and faster method, compared to an earlier proposed Markov network which works
iteratively by applying Belief Propagation [73]. They proceed in scan-line order to
match contrast normalized overlapping patches of the input to a database of training
images. Thus, spatial consistency between patches is enforced to the left patch and
to the previous line only. To measure similarity, the L 2 -norm is used.
Hertzmann et al. [95] applied a supervised filter design method that they termed
'image analogies' to the super-resolution task. The method works also in scan line
order, but uses a multi-scale image synthesis approach. They use a distance measure
that enforces spatial consistency. The approach is also applicable to texture transfer
tasks and to generate artistic image filters.
All of the above three methods generate plausible image detail from low-
resolution images. Although they build data structures, such as trees, from the train-
ing set, the models used are very complex and thus need much memory to store
many free parameters and require intensive computations to find the best matching
training example.
In the following, I show how to condense the information present in the training
examples into the few parameters of a hierarchical recurrent neural network through
supervised learning. The effort of training the network pays off during the recall
phase.
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