hardware implementation of data compression ... - INFN Bologna

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or, expressed as a matrix:
Data compression techniques
C = ASA T
The inverse transform is the following one:
S = BCB T
(2.25)
(2.26)
Frequently orthonormal transforms are used, so that B = A −1 = A T ,
in a way that calculating the inverse trasform reduces to:
S = A T CA (2.27)
Even in the bi-dimensional case, in order to reach a high compression
ratio, a good transform has to be chosen. For instance the JPEG
standard has adopted, until the year 2000, the use of the Discrete
Cosine Transform, known as DCT.
If A is the matrix representing the DCT, the following relationship
follows:
(2j +1)iπ
[A]i,j = w(i)cos
j =0, 1,... ,N − 1 (2.28)
2N
where:
⎧
⎨
w(i) =
⎩
1
N
2
N
i =0
i =1,... ,N − 1
Fig. 2.3 gives a graphical interpretation of (2.28).
After choosing the transform, the next step consists in the quantization
of the transformed image.
Several approaches are possible: for example the zonal mapping foresees
a preliminary analysis of the transformed coefficients statistics and
alaterassignmentofafixednumberofbits.
The name zonal mapping comes from the assignment of a fixed number
of bits depending on the zone in which each coefficient is placed in the
square N × N block under study; Tab. 2.6 reports an allocation bit