Applications of Emergent Phenomena - Systematic Design for Emergence in Cellular Nonlinear Networks - page 148

scheme while noting down the PSNR (power signal to noise ratio) obtained in
each case as a performance measure. The test images are the same.
The result may be summarized as follows: The best gene is ID 107

(PSNR = 24.6 dB for 0.3 bpp) while for a list of other ten genes the PSNR perform-
ance decreases with no more than -1 dB: ID = 11, 27, 43, 67, 75, 83, 103, 135, 920,

952. In terms of local Boolean function complexity, all 11 above except ID = 103
and ID = 920 require m = 3 transitions (see Table 3.3 in Chap. 3). The two excep-
tions are linearly separable Boolean functions ( m = 1 transition) and therefore they
would be better choices to simplify the implementation.
The emergent patterns used for codebooks (including their power spectrum
in logarithmic scale) for some of the above “fast codebooks” are presented in
Fig. 8.14.

Fig. 8.14. Several codebooks and their power spectra (ID numbers and number of iter-

ations are indicated in the upper row )

The above sieve was also applied to the 2s9 CA family in an attempt to im-
prove the PSNR. However, no improvement was found although now the choice
list is much larger (1,488 candidates). The best PSNR (24.5 dB) was obtained for
ID = 2,975. A list of other 48 IDs giving a PSNR, which deviates with no more

than 1 dB was extracted. Such a member of it is for instance ID = 15,375.

Another set of genes (called “ slow codebooks ”) are selected if we tune the
sieves for long transients where the clustering index is slowly increasing from

C = 0.5 to 1. By properly choosing the number of iterations till stop T optimal
codebooks for the CA-VQ method may be obtained.

The following (triple) sieve was used to detect long transients: (implod- U 1

ing patterns) AND (relatively long transients) AND (low spatial L ! 0 C ! 0

frequency at the end).
When applied to the 2s5 family the result is a list of 18 genes: ID = 76, 92, 131,
139, 147, 171, 179, 187, 203, 219, 791, 823, 836, 837, 852, 857, 884, 889. The
“slow codebooks” have an advantage over the “fast” ones (introduced previously)
in that they can be finely tuned by properly choosing the stopping iteration. They