IEEE Geoscience and Remote Sensing Magazine - September 2014 - 18

(a)

(b)

(c)
Figure 11. AVIRIS Yellowstone uncalibrated Sc0 band 99. Images
have been magnified and sharpened so that artifacts are more visible. (a) Original, (b) 0.1 bpppb, and (c) 1.0 bpppb.

C X yields the transform matrix V. This transform can
be used as spectral decorrelator in conjunction with any
monoband compression algorithm to be applied to each
transformed spectral channel (eigenimage). Since eigenimages have different energy, though, the problem arises to
allocate the available bit-rate budget to the monoband coding of each eigenimage. Indeed, much like bit allocation is
18

necessary in 2D compression of a single image, it is all the
more necessary in the multiband case, in which not only
different units in one transformed band may have different
energy, but different transformed spectral channels may
also have different energy. In the following we describe
the specific approach taken by JPEG2000, which is based
on post-compression rate-distortion optimization. Other
approaches are also possible, based on JPEG2000 [39] or
other coding techniques employing, for example, zerotrees
[46], [47].
In particular, JPEG2000 employs the concept of codeblocks, which are similar to the 8 # 8 blocks in CCSDSIDC. A codeblock, whose size is defined by the user but
cannot be larger than 212 wavelet coefficients (and always
within the same wavelet subband), is the basic unit that is
encoded independently. Encoding in JPEG2000 is based
on an approximated binary arithmetic coder called MQ
coder [7] that is applied independently to all bit-planes
of each codeblock. First, encoding of the whole image
is performed at a relatively high bit-rate. During this
process, rate-distortion information is collected regarding each independent coding unit in the 3D transform
domain, based on how many bits have been employed
by the MQ coder to encode each unit, and what is the
contribution of that unit in reducing the distortion of the
decoded image. Then, this information is used in order
to sort all units in decreasing order of their rate-distortion importance. Finally, coded units are picked from the
sorted list and are written in the codestream until the
target rate has been achieved. This allows to obtain a rate
very close to the desired target. The computational complexity of this process is however rather high, since the
algorithm employs an entropy coder whose complexity
is not negligible, and uses it to encode data at a rate even
higher than the final rate of the codestream. It should be
noticed, however, that the rate-distortion optimization
procedure is not a mandatory part of the JPEG2000 standard, and simpler techniques could be used, although
they would entail a performance loss with respect to the
technique described above.
D. Multi-coMponent experiMents
We now here report the progressive lossy-to-lossless coding
performance of several multi-component coding techniques
for the images in the considered data set. Fig. 12 and 13
provide a rate-distortion comparison between two coding
standards, classical JPEG2000 [29] and CCSDS-IDC, when
coupled with a KLT applied on the spectral dimension.
The parameter setting and the software used for this
experiment have been already discussed in previous sections.
Fig. 12 illustrates the benefits of using a multi-component transform (KLT) on an uncalibrated image. As soon
as bitrate increases over 0.5 bpppb, applying a KLT along
the spectral dimension boosts the coding performance by
about 20 dB. This boost is dependent on the image being
coded, with some image yielding higher gains than others.
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