Applications of Emergent Phenomena - Systematic Design for Emergence in Cellular Nonlinear Networks - page 146

For the entire bitplane m this error is evaluated as a bit error percentage
Berr(m) i.e. the fraction of erroneous bits in the reconstructed image. Such errors
produce “salt-and-pepper” noise in the reconstructed image, requiring some
additional steps of Median filtering [97] applied to the reconstructed image. Such
errors are visible mostly when they occur within the most significant bitplanes.
Fortunately the bit error percentages are lower in these bitplanes and consequently
Median filters are quite efficient. The quality of the overall encoding-decoding
process is evaluated by the PSNR 1 of the recovered image (in comparison to the
original).
The compression efficiency is expressed as a “bits-per pixel” (bpp) rate. In a
bitplane “ k ” each index J is represented with log bits. We assume next the

most general structure of our scheme, with different codebooks and window sizes
per each bitplane k . For the CA-VQ algorithm the bit-per-pixel rate can be com-
puted as:

C

k

2

m

log C

2 k

(8.1) bpp

¦

2

w

k 1

k

For instance, if m = 4, the compressed image is represented with 0.5 bpp if
C = 256 and w = 8 for all bitplanes.
Better compression can be achieved using an entropic coding. This scheme will
be called CA-VQ-E in the next and requires further encoding of indexes J using
the Huffman's algorithm taking in consideration different entropies of the indexes

J . For m = 4 and for the image shown in Fig. 8.12 the pixel rate decreases from

0.5 bpp in the non-entropic case, to only 0.2934 bpp, for the entropic encoding.

Fig. 8.13. The principle of the decoding (decompression)
1 The power signal to noise ratio (expressed in dB), where the noise signal is the
difference between the original and the recovered image.