IEEE Geoscience and Remote Sensing Magazine - September 2014 - 12
Next we will provide a brief overview of this recommended standard and then we will show its coding performance for lossless compression as compared to other
coding techniques.
A. The CCSDS-123 ReCommenDeD STAnDARD
As is the case for the previous Recommended Standard
for mono band lossless and lossy data compression issued
by the CCSDS in November 2005, CCSDS-122 [11], the
CCSDS-123 standard defines the encoding process and
is also structured in two functional parts (see Section III
below). Fig. 3 illustrates these functional parts.
In the first stage, a predictor is used to estimate the value
of the current pixel based on previously visited pixels. In
the second stage, an entropy encoder is applied to achieve
data compaction. This second stage can be carried out on
a sample-adaptive or on a block-adaptive basis. Block-adaptive
entropy encoding had been already employed in the first
CCSDS Recommended Standard for data compression,
intended for mono band image lossless compression [12]
and issued in May 1997. Although block-adaptive encoding is not as efficient as sample-adaptive encoding, it is also
contemplated to favour still-in-use implementations of the
former standard.
1) Predictor
Regarding the first stage, the predictor is asked to provide
an estimation or prediction of the current pixel based on
previously scanned pixels. Given the original pixel x i, j, k (row
i, column j, component k) and the predicted pixel Kx i, j, k a
prediction error e i, j, k can be computed, similar to the classical definition e i, j, k = x i, j, k - Kx i, j, k . This prediction error is then
mapped to a non-negative integer m i, j, k, named mapped prediction residual. As seen in Fig. 3, these mapped prediction
residuals are passed to the second stage, the entropy coder.
The predicted pixel Kx i, j, k is estimated based on neighboring pixels, both in a spatial or in a spectral sense. These neighboring pixels are combined to produce a local sum v i, j, k . When
Input Image
it is expected that the sensed signal has a larger correlation in
the vertical direction, only the pixel above the current pixel
is employed to compute the local sum; otherwise, four spatial neighbors are used. As mentioned, in addition to spatial
neighbors, spectral neighbors from P previous bands, with
P ! {0, .., 15}, might also be taken into account.
Fig. 4 illustrates the spatial neighbors used to compute
the local sum. In case of a neighbor-oriented local sum,
v i, j, k is computed as the sum of the four spatial neighbors,
v i, j, k = x i -1, j -1, k + x i -1, j, k + x i -1, j +1, k + x i, j -1, k . In case of a column-oriented local sum, v i, j, k is computed as four times
the pixel immediately above the pixel to be predicted,
v i, j, k = 4 $ x i -1, j, k . For pixels in the border of the image, the
computations are adapted accordingly.
This local sum v i, j, k is then scaled and used to predict
pixel x i, j, k . The local sum is a preliminary estimate of the
to-be-predicted pixel, and, as it might be not accurate
enough, the difference between the computed local sum
and their corresponding-scaled-original pixel is tracked
and stored in a local difference vector U i, j, k for some samples.
There are two possible prediction modes, full or reduced,
depending on whether both spectral and spatial neighbors
are considered, or only spectral neighbors. In mathematical
form, the local difference vector U i, j, k for the full prediction
mode is expressed as
R N V R
V
S d i, j, k W S 4 $ x i -1, j, k - v i, j, k W
S d W W S 4 $ x i, j -1, k - v i, j, k W
S i, j, k W S
W
S d iN, jW
S4 $ x i -1, j -1, k - v i, j, kW
,k W
S
W S
W
U i, j, k = Sd i, j, k -1W = S4 $ x i, j, k -1 - v i, j, k -1W .
Sd i, j, k -2W S4 $ x i, j, k -2 - v i, j, k -2W
S
W S
W
S h W S
h
W
SS
WW S
W
d i, j, k -P
4 $ x i, j, k -P - v i, j, k -P
X
T
X T
xi-1, j-1, k
xi-1, j, k
xi, j-1, k
xi, j, k
(a)
Predictor
Mapped Prediction Residuals
xi-1, j-1, k
xi-1, j, k
Encoder
xi, j-1, k
xi, j, k
Encoded File
12
xi-1, j+1, k
xi-1, j+1, k
(b)
Figure 3. CCSDS MHDC functional parts: prediction followed by
Figure 4. Pixels used to calculate the local sum v i, j, k . (a) Neighbor-
encoding.
oriented local sum and (b) column-oriented local sum.
ieee Geoscience and remote sensing magazine
SEPTEMBER 2014
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