IEEE Geoscience and Remote Sensing Magazine - December 2021 - 111

precise estimation of the input data statistics. The ratio
z ()/( )tt
RCu
entropy symbol. More specifically, ()tz
entropy if and only if
RC$
u
z ()·(),tT t2·
14
determines whether a sample is a high- or lowd
is
defined as high
(19)
where T0 is a constant provided in the standard. This definition
allows for image regions that are well predicted to be
coded with low-entropy codes and using the high-entropy
mode otherwise.
Each high-entropy sample is encoded using a family
of reversed-length-limited GPO2 codes. As in the sampleadaptive
case, each code is identified by an index, ().ktz
For the hybrid coder, ()
ktz
that satisfies
#
CR#
()
t
dd0lzk()z tz
d
2 tt
22
ktz
kt
()
max D◗
If6@d tU2 ()
ktz
1
z (),t
is defined as follows:
z()
max
z ()/, 0 dlkt z
◗ Otherwise, (( ))t
d
0 dlkt z
resentation of ()tz
(, ),
z 25()+
z() + 49 2
u 6@ (20)
C()/.
The codeword emitted for the high-entropy sample
(),( ())tt
then (( ))t
consists of the
ktz () least-significant bits of the binary representation of
followed by a one, followed by ()/t 2 ()
z()
6@zd
ktz
followed by Umax
zeros.
consists of the D-bit binary repzeros.
The
low-entropy samples are processed with one of 16
available variable-to-variable-length codes. The code index
used to process a low-entropy sample ()tz
satisfying
d
RC ##
u
zi
14
20 15
1
where ,,
TT
()·()· ,,tt Ti
is the largest i
(21)
015f are constants provided in the standard,
and T0 is used in (19). This definition allows for the magnitude
of recent prediction errors to determine the next
variable-to-variable-length code to be used.
Each code i has a prefix of previously input samples.
When a sample is processed, a symbol is added to the corresponding
code's prefix. The standard defines a list of complete
prefixes for each code. At this point, if code i's prefix
matches any of those complete prefixes, a codeword that
uniquely identifies that prefix and its associated sequence
of input samples is emitted. After that, the prefix for that
code is cleared.
It is worth noting that the complete prefixes defined for
code i cannot contain sample values satisfying ()d 2
where ,,
zi
LL
tL ,
015f are constants defined in the standard.
When such a sample is processed, i.e., referred to as an unlikely
sample, (())
0 d -l
zi
symbol X is added to the prefix instead of ().tz
tL 1 is emitted, and an escape
d
Adding
X to any code's prefix is guaranteed to make it complete
and trigger the emission of an output codeword. The input
symbol limit Li limits the size of the input alphabet in the
low-entropy codes by treating all of the unlikely symbols
in the same way. This enables us to reduce the number of
DECEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
is the largest positive integer
codewords in a code. As escape symbols occur with low
probability, the efficiency with which these residual values
are encoded has only a small impact on the overall coding
effectiveness.
COMPRESSION PERFORMANCE
EXPERIMENTAL SETUP
The lossless and near-lossless compression performances
of Issue 2 are explained in this section. The results are
provided for both the block- and sample-adaptive entropy
coders already present in Issue 1 and are compared to those
of the new hybrid coder defined in Issue 2. The hybrid
coder's computational complexity is comprehensively addressed
in [69], so the execution time results are not presented
here. The empirical results were obtained using a
varied corpus of 17 multispectral images, 38 hyperspectral
images, and two sounder data samples. These were generated
by 14 different instruments deployed in real missions,
except for the Pleiades images, which are simulated. Most
of the images included are raw, giving more weight to the
direct compression of images as they are acquired, while
the nonraw instances processed after acquisition are also
included to represent some possible onboard calibration.
Both pushbroom and whiskbroom sensors are covered
in the corpus and include the streaking artifacts that are
characteristic of pushbroom instruments (such as Hyperion)
in uncalibrated images. A diverse range of spectral
separations is considered, and examples of images with
significant noise levels (the Moon Mineralogy Mapper) or
that are acquired with airborne instruments [the Compact
Airborne Spectrographic Imager (CASI)] are included as
well. Regarding the dynamic range, all the hyperspectral
and sounding instruments produce data with bit depths
of at least 11 bits, whereas, for multispectral instruments,
samples of lower bit depths are available, too.
A summary of this corpus, produced by the CCSDS MHDC
Working Group, is provided in Table 3. All of the images are
publicly available, except for those produced by the Infrared
Atmospheric Sounding Interferometer (IASI) and Meteosat
Second Generation instruments, due to licensing restrictions.
(The download links for the test images can be found
at http://cwe.ccsds.org/sls/docs/sls-dc/123.0-B-Info/TestData.)
The " Entropy " column in the table represents the zero-order
entropy of the images. Note that this is not a strict bound on
compression efficiency and should be regarded as only an assessment
of the difficulty of compressing the images.
The performance results are obtained by invoking Issue
2's compressor with the default set of parameters described
in [37], except for the Hyperion, IASI, Moderate Resolution
Imaging Spectroradiometer (MODIS), and Système Pour
l'Observation de la Terre 5 (SPOT5) instruments. For these,
the following parameters are modified to enhance compression
performance:
0 4 .
tv vUcmin
== == =c *
maxmax
9,, ,,
in 20 32 11
and c = A full prediction with wide, neighbor-oriented
local sums is used in most of the images, including the
111
http://cwe.ccsds.org/sls/docs/sls-dc/123.0-B-Info/TestData
IEEE Geoscience and Remote Sensing Magazine - December 2021

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