Page 135 - 2023-Vol19-Issue2

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TABLE III.
AVERAGE COMPRESSION RATIOS OF BIT PLANES FOR DIFFERENCES
IN THE HSI CHANNELS FOR THE ARITHMETIC CODER
Bit planes Partial (full) compression ratios Bit planes Partial (full) compression ratios
(high/low) high/low of bit planes of images (high/low) high/low of bit planes of images
15/14–0 0.5706/2.4806 (2.0414)
14/13–0 15.6852/2.3152 (2.6180)
14–13/12–0 31.3705/2.1498 (2.6180)
14–12/11–0 47.0557/1.9844 (2.6180)
14–11/10–0 62.7409/1.8191 (2.6180)
14–10/9–0 78.4262/1.6537 (2.6180)
14–9/8–0 94.1114/1.4883 (2.6180)
14–8/7–0 109.7933/1.3235 (2.6191)
not effective. In other cases, the arithmetic coder provides
compression of individual bit planes and their combinations.
Moreover, when coding the higher bit planes of differences in
the HSI channels, the arithmetic coder shows the worst results
in comparison with the RLE coder.
When coding test images in their entirety (without sepa-
ration into bit-planes) using the arithmetic ( fAC (I (R))) and
RLE ( fRLE (I (R))) coders, the following average compres-
sion ratios were obtained: satellite images – CRAC =1.22 and
CRRLE = 0.95 times; portrait images – CRAC =1.35 and CRRLE
=1.04 times; medical images – CRAC =1.86 and CRRLE =1.62
times; landscape thermal images – CRAC =2.13 and CRRLE
=1.69 times; differences of HSI channels – CRAC =2.29 and
CRRLE =1.02 times. The comparison of these results with
the data given in Tables (I, II, and III), shows that sepa-
rate coding of bit planes ( fRLE (B (r)) at r = 0, R - 1 and
fAC (IC (rHL, rHH )) , fAC (IC (rLL, rLH )) at rHH = R - 1, rHH >
rHL, rLH = rHL - 1, rLH > rLL, rLL = 0) allows to increase the
compression ratio of images compared to their direct coding
( fRLE (I (R)) and fAC (I (R))).
III. COMBINED EFFECTIVE CODING OF
IMAGE BIT PLANES
To increase the lossless image compression ratio, the com-
bined effective coding is used. Its essence consists in us-
ing to compress the highest image bit planes or their com-
binations, several coders of various types ( fRLE (B (r)) and
fAC (IC (rHL, rHH ))), better taking into account the distribu-
tion of their values, and directly incorporate in the coding
result of the lower bit planes ( fNC (B (r)) at r = 0 or
fNC (IC (0, rLH )) at rLH = 0), the coding of which is not ef-
fective (? fRLE (B (r))? = Y X at r = 0 or ? fAC (IC (0, rLH ))? =
(rLH + 1)Y X at rLH = 0), as shown in Fig. 3, where fNC –
is the direct transfer function of the lower bit planes without
coding.
Tables (I, II, and III) show that combined coding is effec-
Al-Furaiji, Tsviatkou & Sadiq
14–7/6–0 119.2902/1.1660 (2.6355)
14–6/5–0 92.6252/1.0025 (2.6136)
14–5/4–0 94.0904/0.8537 (2.6491)
14–4/3–0 93.4257/0.7415 (2.7321)
14–3/2–0 22.6167/0.6888 (2.9558)
14–2/1–0 6.5078/0.6497 (3.0008)
14–1/0 3.9643/0.6073 (3.0477)
Fig. 3. Combined effective coding of image bit planes scheme
tive for compressing the differences of HSI channels.
HSI P = {P (i)}(i=0,NC-1) is a collection NC of spectral
channels P (i) = ?P (y, x, i)?(y=0,Y -1,x=0,X-1) of size Y × X
pixels and bit depth DB. Each spectral channel corresponds to
a specific part of the spectrum.
To estimate the pixel correlation of the i–th P (i) and j–th
P ( j) HSI channels, the values of mean error MEP (i, j) are
used, which is calculated using (8).
Y -1 X-1
MEP (i, j) = ? ? |p (y, x, i) - p (y, x, j)| / (Y X) (8)
y=0 x=0
where | | – is modulo operation.
Fig. 4(a) shows the dependence of MEP (i, j) on the spec-
tral channel number at i = 24 and j = 0, NC - 1, NC = 68.
To estimate the bitwise correlation of the b-th bit planes of
the i–th P (i) and j–th P ( j) channels of hyperspectral images
HSI, the values of mean error MEB (b, i, j) are used, which is
calculated using (9).
MEB (b, i, j) = ?Yy=-01 ?Xx=-01 (p (y, x, b, i) ? p (y, x, b, j)) (9)
YX
where ? – operation «Exclusive OR».