IEEE Geoscience and Remote Sensing Magazine - December 2021 - 108
t
v =+ +mm msss .11 1
zyxzyx
,, ,, ,, ,,
-- -- +
11 zy xzyx
2
(9)
As can be observed in Figure 3, column-oriented local
sums employ sample representatives at the same x coordinate,
whereas neighbor-oriented sums also use sample representatives
at contiguous x coordinates. In turn, the new
narrow option removes the dependency on
m
s ,,
zy x 1- which
,
facilitates pipelining in a hardware implementation at the
cost of some compression performance loss [37]. Note that
wide and narrow column-oriented modes are identical in
the general case. Notwithstanding, only the wide columnoriented
mode uses s ,,
,
m
zy x 1for
calculating local sums at the
first row, i.e., y 0= of each spectral band.
Local differences are computed based on the sample representatives
and the local sums. For an input sample s ,,
zy z
zy x
,
up to four local difference types are computed: the central
difference d ,,
north d ,,
zy x
^hN
, west
d
d
d
d
N
zy x
^hW
d ,,
zy x
zy x
zy x
W
zy x
NW
,,
,,
,,
,,
=
=
=
=
4
4
4
4
d ,,
zy x
NW
.
defined as follows:
s
s
s
s
m
m
m
m
zyxzyx
zy
,,
,,
zyxzyx
zy xzyx
,, -1
-
-
v
v
,,
,,
-- -
,
,
11 v ,, .
(10)
The predicted sample value is then computed using either
the full or reduced prediction modes. In the full prediction
mode, the local difference vector U ,,
directional differences from the current spectral band and
central differences from the previous bands:
U ,, dddd d
zy x = 6 ,,, ,,zyxz Py x@.
zyx
N
,,
zy x
W
,,
zy x
NW
,, -- ,,
1,, f
(11)
In the reduced prediction mode, the local difference vector
uses only central differences from previous bands:
U dd .
zyxz yx1,, f
,, = --6
,,
zP yx@
,,
In both modes, a prediction weight vector W ,,
(12)
zyx is used to
obtain a weighted sum of local differences, called the predicted
central local difference, as
zy x is defined using
,, - v ,, ,
-1 x
zyx
^h and three directional differences, i.e.,
, and northwest ^h They are
where Ω is a parameter that controls arithmetic precision.
The initial prediction weight vector for each band,
can be defined based on default or user-provided
W ,,,z 00
values. In either case, vector elements are updated after
processing each input sample ().stz
The updates are based
on the obtained prediction error and several user-defined
parameters, namely, ,, ,,vv
minmax gg and t ,inc which con()
*
z
i
z
trol the rate at which weights are adapted to the original
image statistics. More precisely, the smaller values of
,, ,,
ggz
i
() *
z vv and /t1 inc
minmax
typically produce larger weight
updates. This results in a faster adaptation to the source
statistics at the cost of worse steady-state compression performance
[37].
It is important to highlight that the existence of two prediction
modes (full and reduced) as well as two different
local mean types (column and neighbor oriented) is present
in Issue 2 so that prediction is effective for the image
data produced by different types of instruments. For instance,
when streaking artifacts are present in the images,
reduced column-oriented prediction tends to produce the
best results [37].
QUANTIZER INDEX MAPPING
The prediction errors ()tz
D obtained in (1) as well as their
qtz
zy x
=
d WU,,
zy x
T
,,
zy x,, .
(13)
The predicted sample is then calculated as an integer approximation
to
t
,,
s
zy x,, .
+ v
X
t
IEEE Geoscience and Remote Sensing Magazine - December 2021
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