Cellular Automata for Efficient Image and Video Compression - Cellular Automata in Image Processing and Geometry - page 5

Fig. 1.2 Organization of signals in b binary sequences called bit-planes . Bitplane j is as-
sociated to the binary sequence s k , k = 1 ... K . Each sample s k is represented on b bits. s k =
[ with s k ε {

s k , s k ,···, s b − 1

k

] 0 , 1 } (binary).

In Section 1.4 an efficient method to implement CA systems in FPGA technologies
is briefly discussed in relation with the representation of the CA local rule using
Algebraic Normal Form (ANF).

1.2 An Alternative to Compressive Sensing Based on Cellular

Automata Scan

1.2.1 Principle of Chaotic Scan

This approach to message compression is a compact alternative to the compressive
sensing methods [1] and was first proposed in [19]. The simplified model is given
in Fig. 1.3, with regards to an image sensor. The idea may be further expanded
to any other kind of multi-dimensional sensor in order to reduce the number of
samples effectively transmitted from the sensor. The method is effective assuming
that adjacent elements in the image array are highly correlated.
The nonlinear dynamic system (discrete-time, discrete-state) present in both Tx
(encoding) and Rx (decoding) units can be any kind of automaton as long as it en-
sures certain properties to be detailed next. Since its role is to address (count) K pix-
els (or in general, K samples) from the N samples of the original message it will be
called next a “chaotic counter”. The term “chaotic” is a simplification from “pseudo-
random”, the above mentioned system implementing in fact a pseudo-random num-
ber generator. As discussed next in more detail, a convenient chaotic counter belongs
to a class of 1-dimensional cellular automata having all desired properties for such a
system. The contrast with a raster scanning counter is exemplified in Fig. 1.4. Here
only 5% of the pixels in the original image) were addressed sequentially during the