Information Technology Reference
In-Depth Information
Fig. 12.25
(
a
) Reconstructed Boats image achieved by a one hidden layer FNN with sigmoidal
basis functions, (
b
) Reconstructed Boats image achieved by an FNN with Hermite basis functions
where the first term in the denominator is the number of outputs of the hidden layer
with respect to all input patterns, and the second term is the number of the output
weights.
In the sequel the image compression performed by FNN with Hermite basis
functions is compared to the compression achieved by an FNN with sigmoidal
activation functions. The hidden layer nodes of the FNN with Hermite basis
functions contains the first 4 eigenstates of the quantum harmonic oscillator given
in Eq. (
12.10
). Both neural structures consist of 16 nodes at the input layer, 4 nodes
at the hidden layer, and 16 nodes at the output layer.
Tests are performed on two benchmark images, Lena and Boats. Both images are
of size 512512 pixels and the block size is selected as 44.UsingEq.(
12.28
), the
compression ratio achieved by the examined neural structures is found to be '4.
The reconstructed Lena images are depicted in Fig
12.23
a,b and in Fig.
12.24
a.
The reconstructed Boats images are depicted in Fig
12.24
b and in Fig.
12.25
a,b,
respectively.
12.8
Applications to Fault Diagnosis
12.8.1
Signals Power Spectrum and the Fourier Transform
It will be shown that neuronal networks using as activation functions the QHO
eigenstates can be also used in fault diagnosis tasks. Apart from time-domain
approaches to fault diagnosis, one can use frequency-domain methods to find out
