IEEE Geoscience and Remote Sensing Magazine - December 2021 - 114

observed that Issue 2's hybrid coder enables higher image
quality, i.e., a lower PAE, at similar, albeit smaller,
compressed data sizes. Furthermore, for sufficiently low
PAEs, reconstructed images are hardly distinguishable
from the originals. In turn, the bottom row illustrates
how moderately larger PAEs introduce some texture artifacts,
but retain the image's structure, and so might not
hinder analysis tasks performed on it [30], [31]. A visual
inspection of this row also reveals that Issue 2 introduces
distortion patterns similar to those of JPEG-LS. This is expected
because both algorithms apply quantization after
prediction. It is worth noting that the choice of entropy
coder in CCSDS 123.0-B does not affect the obtained reconstructed
image, only the compressed data size. Compressed
data rate differences aside, a similar discussion
regarding visual quality applies for M-CALIC, too. It is
omitted here for space constraints.
The remainder of this section provides quantitative
discussion of the compression performance of the aforementioned
algorithms in relation to the fidelity of the
reconstructed images. For each compressor, PAE, and input
image I, the compressed data rate expressed in bits per
sample (bps) is computed as
compressed data rate =
compressed data size (bits)
NN N··
XY Z
is defined as
10
.
(23)
In turn, the peak SNR (PSNR) between I and its reconstructed
counterpart It
PSNR(, )·t =10 log dnt
2
II
21 ,
D
-
MSE( ,)
MAX
I
II
(dB).
(24)
Here, MAXI denotes the dynamic range of an image, i.e.,
where D is I's bit depth, and mean square error
(MSE)( ,) is the mean squared error between I and I ,t
IIt
NX NY NZ
MSE( ,)=
II NN N
II
t
y
z
··
,,
///^htzy x
x
XY Z
zyx
- ,,
.
(25)
2
i.e.,
(a)
(b)
(c)
(d)
(e)
(f)
FIGURE 7. (a) A crop (256 × 256) of Band 220 of an original AVIRIS f060925t01p00r12_sc00 image (calibrated, 16 bit); (b) and (c) the colocated
crops of the same AVIRIS image after reconstruction with CCSDS 123.0-B-2's hybrid coder [compressed at 2.4 bits per sample (bps)]
and JPEG-LS (2.9 bps) with absolute error limits of 2 and 16, respectively; (d) a crop (128 × 128) of an original SPOT5 toulouse_spot5_xs_
extract1 image (processed, 8 bit); and (e) and (f) the colocated crops of the same SPOT5 image after reconstruction with CCSDS 123.0-B-2's
hybrid coder (1.1 bps) and JPEG-LS (1.4 bps) with an absolute error limit 12. The brightness and magnification have been adjusted in all of
the images to facilitate a comparison. The SPOT5 images are presented using false color.
114
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