Image Processing Reference
In-Depth Information
original message is preserved (yet scrambled) without compression i.e. K =
N .In
fact, the user-selected K parameter represents the number of cycles advanced by the
properly designed CA used in chaotic scan and can be traded off for the quality of
the reconstructed message.
Compared to the CA-based A-stage, in terms of functionality, the closest ap-
proach found in the literature seems to be the “holographic scan” [3] although the
implementation of this algorithm appears to be more complex than implementing a
cellular automaton. Other traditional approaches implementing stage-A are the use
of various image transforms (requiring intensive arithmetic computations) such as
DCT, Karhuenen-Loeve or PCA, kernel-PCA [26] [28] or neural auto-encoders [23].
Stage-B is basically a Vector Quantization (VQ) stage. Blocks of the original
message (or compressed, resulting from the A-stage) are m -sized vectors that would
be compared with codebook vectors in a D -sized dictionary (previously prepared
to optimize the compression efficiency for a class of messages). Consequently a
label (among all D possible) is selected indicating the closest codebook vector. Tra-
ditional approaches to VQ employ computationally intensive arithmetic operations
performed in fixed-point representations of the variables (including message sam-
ples). In contrast, our CA-based approach, to be detailed in Section 1.3, has two
simplifying features: i) the message is divided in binary bit-planes (i.e. binary
message sequences associated to one rank bit in the original sequence) as seen in
Figure 1.2 such that m-sized vectors are now m-bit binary words; ii) the codebook
is a list of m-sized binary vectors , generated by a 2-dimensional CA with a certain
rule. The CA rule may be obtained using a training approach (as detailed in this
chapter) or it can be the result of a selection process [21] [11]. In effect, computa-
tionally intensive arithmetic operators are replaced with simple logic operators and
the codebook is simply generated based on CA rule information only (there is no
need to send the entire codebook from Tx to Rx). In terms of performance (evaluated
here as the PSNR - Power to Signal Noise Ratio - between original and recovered
message) the CA-VQ approach is comparable to traditional image compression al-
gorithms (e.g. JPEG) and in fact is more effective for low bit-rates (under 0.25 bits
/ sample). An FPGA implementation is reported in [32].
Mixed approaches involve exploiting both A and B stages. For instance, one may
scan only K
N samples from the original message and submit to the VQ system an
incomplete m -sized vector (some bits are not specified since they belong to samples
that were not scanned). Still a codebook search can be performed for the best match
and the result is an improved compression rate (with an N
<
/
K factor) at a slightly
degraded PSNR performance.
In order to implement the proposed compression methods various technolo-
gies may be used. Of a particular interest is the possibility to embed compres-
sion algorithms into smart sensors with low power requirements. Consequently,
it is important to choose convenient synthesis solutions such that the whole al-
gorithm is described in a hardware description language (e.g. VHDL or Verilog).
 
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