Page 136 - 2023-Vol19-Issue2

132 |
For example, in Fig. 4(b, c, d) are shown the dependences
of MEB (b, i, j) on the spectral channel number at i = 24, b =
{12, 5, 0} and j = 0, NC - 1, NC = 68.
Fig. 3 shows that, HSI bit planes have different correlation
properties. Higher planes determine the general form of the
error distribution function, while lower planes practically do
not correlate and slightly affect the general form of the error
distribution function.
Table IV shows the most effective combinations of arith-
metic and RLE coders for the bit planes of the four differences
of adjacent channels of the test HSI taken from the Aviris
database [24], and the compression ratios CRC, corresponding
to these combinations.
The compression ratio for combined effective coding is
calculated using (10).
RY X (10)
CRC = S1 + S2 + S3
where S1, S2, S3 are calculated by using the expressions (11),
(12), and (13) respectively.
M (11)
S1 = ? ? fRLE (B (r (m)))?
m=1
N (12)
?S2 = ? fAC (IC (rL (n) , rH (n)))?
n=1
P-1 (13)
S3 = ? ? fNC (B (p))?
p=0
at R = M + N + P, rH (n) > rL (n), M = 0, N = 0, P = 0,
where M – is the number of bit planes encoded using the
RLE coder; N – is the number of bit planes encoded using
the arithmetic coder; P – is the number of bit planes, directly
transferred to the resulting code.
Based on the Table IV, the following rule of combined
coding of differences of neighboring HSI channels is pro-
posed, which determines the formation of the resulting code
CC: it is necessary to use the arithmetic coder for the highest
sign plane and bit planes 8–2, the RLE coder – for bit planes
14–9, transfer without coding – for bit planes 1–0, which is
determined by (14).
CC ? fAC (B (15)) ? fRLE (B (14)) ? · · · ? fRLE (B (9)) (14)
? fAC (IC (2, 8)) ? fNC (IC (0, 1))
it provides the code size ?CC?, equal to (15).
Al-Furaiji, Tsviatkou & Sadiq
14 (15)
?CC? = ? fAC (B (15))? + ? ? fRLE (B (r))?
r=9
+ ? fAC (IC (2, 8))? + ? fNC (IC (0, 1))?
and compression ratio CRC, equal to (16).
16Y X (16)
CRC = ?CC?
where ? – is the concatenation operator, which forms the
resulting code from the fragments, corresponding to bit planes
and their combinations.
From Table IV, it follows that combined coding allows
to increase the compression ratio of the differences of neigh-
boring HSI channels by an average of CRC/CRAC = 1.4 and
CRC/CRRLE = 3.1 times compared to arithmetic and RLE-
coding respectively.
The proposed rule allows to synthesize the structure of
HSI coder as shown in Fig. 5. It consists of a combined coder
of differences of HSI channels and a HSI reference channel
coder. The combination of arithmetic and RLE coders as a
part of the coder of the differences of HSI channels differs
from the effective combinations considered in Table IV, which
leads to a decrease in compression ratio, but does not require
the use of additional switching and control units in codecs.
The gain in the compression ratio of the differences of the
neighboring HSI channels is on average CRC/CRAC = 1.2 and
CRC/CRRLE = 2.6 times compared to arithmetic and RLE-
coding, respectively. To encode the HSI reference channel,
the arithmetic coder is used, to which 12 high-order bit planes
of the reference channel are fed, and 4 lower-order bit planes
are directly transferred to the resulting code. This structure
follows from an analysis of the effectiveness of separate cod-
ing of bit planes of HSI channels, which shows that, as a rule,
from 2 to 6 lower bit planes are not compressed using the
arithmetic coder.
In Tables V, VI are shown the compression ratios of the
higher and lower bit planes for the 24th spectral channel of
16-bit HSI-1, as shown in Fig. 6, and HSI-2 with dimensions
of 2048×614 and 1024×614 pixels, respectively.
Tables V and VI, show that the coding of the lower bit
planes of the spectral channels in some cases is not effective
and the compression ratio of the HSI can be increased by
using the lower bit planes without coding.
The arithmetic coding (AC) blocks are considered the
most computationally complex elements of the HSI coder.
They are operating at frequencies Y XCAC f and Y XCAC f / (N - 1)
in the part of coders of the differences of spectral channels
and reference channel of HSI, respectively, where N – is the