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planes. The efficiency of separate coding of bit planes is
analyzed in [20, 21], but only for the RLE coder [22]. The
results of studying the effectiveness of using a combination of
arithmetic and RLE-coding are presented in [21], but only for
several types of images. Insufficient study of the combined
approach to image coding is associated with an increase in
computational complexity: time (due to the additional cost
of choosing the encoding algorithm) and spatial (due to the
additional memory cost for implementing several encoding al-
gorithms).However, with the development of the element base,
the increase in the computational complexity of coding be-
comes less critical compared to an increase in the compression
ratio, especially for applications involving the transmission of
images in real time through channels with limited bandwidth.
In addition, it is possible to use a combination of codecs with
a complex and simple structure, which leads to a relatively
small increase in computational complexity. The most inter-
esting in this regard are arithmetic [23] and RLE [22] codecs.
The arithmetic codec is a part of the JPEG 2000 codec core
and allows to achieve high image compression ratios. The
RLE-codec has a relatively low computational complexity,
because it has found a widespread use as a part of various
image compression codecs and archivers.
The aim of this work is to develop the structure and study
the effectiveness of a combined codec for compressing images
of various types without loss in the spatial domain, based on
arithmetic and RLE coding algorithms.
II. SEPARATE EFFECTIVE CODING OF BIT
PLANES OF IMAGES
To develop the structure of a combined image compression
lossless codec in the spatial domain, a study of the effective-
ness of separate coding of bit-plane images using arithmetic
and RLE coders was conducted. The essence of separate effec-
tive coding is to use for compression the high and low image
bit planes or their combinations of independent coders of the
same type or one coder connected to the planes alternately, as
shown in Fig. 1.
Fig. 1. Separate effective coding of image bit planes scheme
Bit planes B(r) are formed from the same bits of r pixels
i (R, y, x) of an R-bit image I(R) = ?i(R, y, x))?(y=0,Y -1,x=0,X-1) at r = 0, R - 1, where ? ? – represents the code size calculation
and represent a matrix B(r) = ?b(r, y, x))?(y=0,Y -1,x=0,X-1),
consisting of zeros and ones (b (r, y, x) = {0, 1}), the size
Al-Furaiji, Tsviatkou & Sadiq
Y × X of which coincides with the size Y × X of the original
image I (R). The values i (R, y, x) and b (r, y, x) are related by
(1).
R-1 (1)
i (R, y, x) = ? 2rb (r, y, x)
r=0
at y = 0,Y - 1, x = 0, X - 1.
The combination of multiple rC bit planes (0 < rC < R)
from rL to rH (rH > rL, rC = rH - rL + 1) represents a ma-
trix IC(rL, rH ) = ?iC(rL, rH , y, x)?(y=0,Y -1,x=0,X-1), the values
iC (rL, rH , y, x) of which have rC bits, will be expressed by (2).
rH (2)
?iC (rL, rH , y, x) = 2r-rL b (r, y, x)
r=rL
at y = 0,Y - 1, x = 0, X - 1.
For a special case rH = rL, the equality holds iC(rL, rH , y, x) =
b(rL, y, x).
Tables (I, II, and III) show the average compression ratios
of the bit planes of 8-bit (R = 8) satellite, portrait, medical
grayscale, and landscape thermal images Fig. 2(a), as well
as the differences of spectral channels of 16-bit (R = 16) hy-
perspectral images (HSI), as shown in Fig. 2(b). The RLE
and arithmetic coders (AC) are used for compression. The
averaging of values of compression coefficients is made on 8
test images of each type.
Fig. 2. Examples of images
(a) 8-bit grayscale image; (b) differences of spectral channels
of 16-bit hyperspectral image
The RLE coder is applied separately for each bit plane
( fRLE (B(r)) at r = 0, R - 1), where fRLE – is RLE-coding
function. Based on the resulting code size ? fRLE (B (r))? (in
bits), the partial compression ratios are calculated using the
expression (3).
CRRLE (r) = Y X / ? fRLE (B (r))? (3)
operator.