IEEE Geoscience and Remote Sensing Magazine - December 2021 - 107

calculation (in both the compressor and decompressor) is
performed using sample representatives ()
stz
m
stz
l
qtz
to ().stz
t
in place of the
original samples ().stz
A naive solution to this problem is to use the central
point () of the quantizer bin, whose index () is transmitted
to the decoder. The quantizer bin center () can be
stz
l
calculated as
()
where smin
st st qt mt ss21clip
zz zz() ()·(
and smax
l =+ +
^ht
minmax
ues, respectively, allowed for an input sample and
(, ,)
clip xabb ax
(,
guarantees that () falls within the allowed value range.
However, using the quantizer bin center () as the sample
representative () for prediction does not always ministz
l
stz
l
stz
m
mize
compressed data volume [37]. This is true even for
()
mt ,0= i.e., lossless compression.
z
parameters can be used to adjust the choice of ().stz
m
stz
m
In the CCSDS 123.0-B-2 standard, three user-specified
These
are the sample representative resolution (),H damping (),z
and offset ()z} parameters. Based on them, sample representatives
() are defined as an integer approximation to
z
zz }z
c1
2
z t ()+-stz
HH - H sgn qt mt() () .
z
22
mcstlz()
stz
l
^ zz m
h
and ().stz
t
(8)
Regardless of the parameter choice, the sample representatives
always fall between ()
Parameter H determines
the precision with which representatives are computed.
Parameter z
the representative calculation. In turn, parameter z} establishes
a bias toward ()
stz
l
or (),stz
t
depending on its value.
z
==
Although H is defined for the whole image, z and z} can
be chosen on a band-by-band basis. Setting z}
causes the sample representatives to be equal to ();stz
l
zz 0
the
larger values of zz and/or z} produce representatives closer
z limits the effect of noisy samples in
= minmax(, ))
() ), ,, (6)
are the minimum and maximum val(7)
stz
m
fied
by ().qtz
Note that, depending on the parameter choice,
() may not be contained in the quantizer bin identiThe
empirical results indicate that setting the
damping and offset parameters to values other than zero
tends to provide larger benefits to compression performance
when spectral bands are closer in wavelength and
for images with larger noise prevalence [37].
PREDICTION
The predicted sample value ()
tstz
zP ,, ,zffor
an input sample () isstz
computed causally using sample representatives from spectral
bands
where P 0$ is a user-defined parameter.
Within each band, previous sample representatives are
used to compute local sums. These can be regarded as preliminary,
scaled estimates of the actual sample value. Local
sums, in combination with the sample representatives, are
used to compute local differences. The predicted value ()
tstz
is then calculated using the local sum in the current band z
as well as a weighted sum of local differences from the current
and previous bands. Local sums can be understood as a
local mean subtraction, and prediction as being made in the
mean-subtracted domain. Figure 2 displays an overview of
the prediction process. Its stages are more precisely described
in the following.
Local sums are computed from previous sample representatives
using one of the four available modes. Similar
to CCSDS 123.0-B-1, each mode is either neighbor- or column-oriented.
As a novelty of Issue 2, modes can now be
narrow instead of wide. The sample representatives used to
calculate the local sums depend on the selected mode, as
depicted in Figure 3. In the figure and hereafter, s ,,
to denote the current sample (),stz
zy x is used
which makes explicit the
band index z as well as the spatial coordinates (x, y) within
the band. In all of the modes, the highlighted sample representatives
are multiplied by the factor indicated in the
Figure 3 and added together to obtain the local sum
corresponding to s ,,
v ,,
.
oriented local sums are computed as
zy x
zy x For instance, the narrow neighborSample
Band
z - P
...
Band z - 1
Representation
S″
z-P
...
Sample
Representation
S″
z-1
Sample
Band z
Representation
S″
z
+
+
+
Local
Sums
σz-P
...
Local
Sums
σz-1
Local
Sums
σz
−
Differences
dz-1
Directional
Local
−
Differences
dz
FIGURE 2. An overview of the prediction block in CCSDS 123.0-B-2.
DECEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
107
(Full Prediction Only)
dN
z,y,x, dW
z,y,x, dNW
z,y,x
σz,y,x
Predicted Central
Local Difference
dz,y,x
Inner
Product
dz,y,x + 2Ωσz,y,x
2Ω+2
Prediction
Central
Local
−
Differences
dz-P
...
Central
Local
dz-P,y,x
Prediction
Weight
Vector Wz,y,x
Predicted Value
≈
Sz,y,x
dz-1,y,x
Local
Difference
Vector Uz,y,x
IEEE Geoscience and Remote Sensing Magazine - December 2021

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