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Astronomical Data Analysis Software and Systems VII
ASP Conference Series, Vol. 145, 1998
R. Albrecht, R. N. Hook and H. A. Bushouse, e
Ö Copyright 1998 Astronomical Society of the Pacific. All rights reserved.
ds.
An Optimal Data Loss Compression Technique for
Remote Surface Multiwavelength Mapping
Sergei V. Vasilyev
Solar­Environmental Research Center, P.O. Box 30, Kharkiv, 310052,
Ukraine
Abstract. This paper discusses the application of principal component
analysis (PCA) to compress multispectral images taking advantage of
spectral correlations between the bands. It also exploits the PCA's high
generalizing ability to implement a simple learning algorithm for sequen­
tial compression of remote sensing imagery. An example of compressing
a ground­based multiwavelength image of a lunar region is given in view
of its potential application in space­borne imaging spectroscopy.
1. Introduction
Growing interest in lossy compression techniques for space­borne data acquisi­
tion is explained by the rapid progress in sensors, which combine high spatial
resolution and fine spectral resolution. As the astronomical community becomes
aware of multispectral and hyperspectral imaging opportunities, the airborne
land sensing heritage (e.g., Birk & McCord 1994; Rao & Bhargava 1996; Roger
& Cavenor 1996) can also valuably contribute to future development of the space
related instrumentation and data processing methods. On the other hand the
on­board storage capacity and throughput of the space­to­ground link are lim­
ited, especially for distant and costly astronomical missions. This constrains
direct data transmission and the application of traditional image compression
algorithms requiring computationally unreasonable expense and inputs, which
are not often available on space observatories. In addition, to meet rational
operating of the data transmission channels the raw data need on­board com­
pression prior to their down­linking and an option to compress the data flow bit
by bit as it is generated onbord without preliminary image store.
Intuitively, when dealing with the hyperspectral/multispectral imagery, one
can expect potential benefits from sharing some information between the spectral
bands. As a matter of fact, in the case of high spectral correlations between the
bands much of information is redundant, that a#ords a good opportunity for
application of lossless compression.
This paper focuses on the ability of principal component analysis (PCA) to
reduce dimensions of a given set of correlated patterns and suppress the data
noise through data representation with new independent parameters (Vasilyev
1997). It also implements a simple algorithm, which involves some a priori
information about the spectral behavior of the object being studied through
504

An Optimal Data Loss Compression Technique 505
preliminary learning of the principal components for their further application
for practically lossless image compression in a computationally inexpensive way.
2. Essential Concepts
The starting­point for our approach and for the application of the PCA com­
pression to the multispectral/hyperspectral imagery is a spectral decorrelation
transformation at each pixel of the frame on the scanning line across the bands.
In other words, let us represent a multispectral image set taken in m di#erent
wavelengths as the assemblage of n spectra, where n corresponds to the number
of pixels in each single­band picture. Then, let A be the matrix composed of
the signal values A ij of the i spectrum in the j band.
Obviously, all the data, namely each signal value A ij can be easily re­
stored in the m­dimensional basis simply by the linear combinations of l # m
eigenvectors (principal components) obtained for the covariance matrix AA # :
A ij =
# l
k=1 # ik V jk , where k is the principal component number, V jk is the j­th
element of the k­th eigenvector and # ik is the corresponding eigenvalue at the
i­th spectrum.
Generally, m eigenvectors are needed to reproduce A ij exactly. Never­
theless, PCA possesses an amazing feature for the eigenvalues sorted in value­
descending order: the eigenvectors corresponding to the first, largest eigenvalues
bear the most physical information on the data, while the rest account for the
noise and can be neglected from further consideration (Genderon & Goddard
1966; Malinowski 1977). Thus, utilizing l # m eigenvectors yields a significant
compression of the lossy type and allows the compression rate to be adjusted
according to the specific tasks.
Another important feature of PCA that makes this method suitable for
the remote sensing applications lies in its powerful generalizing abilities (Liu­
Yue Wang & Oja 1993). This feature allows us to describe, using the principal
components obtained on the basis of a relatively small calibration data set, a
much larger variety of data of the same nature (e.g., Vasilyev 1996; Vasilyev
1997).
3. The Data Used
The lunar spectral data obtained by L. Ksanfomaliti (Shkuratov et al. 1996;
Ksanfomaliti et al. 1995) with the Svet high­resolution mapping spectrometer
(Ksanfomaliti 1995), which was intended for the Martian surface investigations
from the spacecraft Mars 94/96, and the 2­meter telescope of the Pic du Midi
Observatory were selected and used for testing the PCA compression. The
12­band spectra (wavelengths from 0.36µm to 0.90µm) were recorded in the
``scanning line'' mode during the Moon rotation at the phase angle of 45 # , so
that the data acquisition method was similar to the spacecraft scanning. The
resulting 19­pixel­wide images were composed of these spectra separately for
each band and put alongside in the gray scale (see Figure 1a), where the lower
intensity pixels correspond to the higher signal level.

506 Vasilyev
Figure 1. Results of the PCA multiwavelength image compression
(a, b) and the whole­band interpolation (c, d). Data courtesy of Yu.
Shkuratov, Astronomical Observatory of Kharkiv University.
4. Implementation
For the initial training of the principal components a sample multiwavelength
scan, indicated with the dashed lines in each of the 12 bands on Figure 1a, was
arbitrarily chosen to produce the calibration. The eigenvectors were obtained
using this scan containing 250 out of the total 4,750 spectra. Then the entire
multispectral image set described above was compressed through encoding the
data with the eigenvalues derived from the least­squares fits using the calibration
eigenvectors. Each spectrum was processed independently from the others to
simulate the real data recording process and without storing all the image in
memory.
We found the six principal components providing the compression rate of
1:2, which are able to represent simply by the linear combinations all the features
of the original data with the di#erences not exceeding the rms error in each
channel. The restored multiwavelength image is shown on Figure 1b.
The calibration eigenvectors allow interpolation for the pixels or even whole
spectral bands, which are a#ected by the impulse noise or other errors. To
demonstrate this possibility we have deliberately excluded one channel in the
original data set from consideration (shown on Figure 1c) and performed the
data encoding with the six principal components. Image restoration made in
the ordinary manner proves such a knowledge­based interpolation to be ideal
for the remote sensing imagery (see the interpolated single­channel image on
Figure 1d).
5. Conclusions
PCA is shown to be applicable to on­board multispectral image compression
allowing the incremental compression preceded by the preliminary calibration

An Optimal Data Loss Compression Technique 507
of the principal components with fairly short learning times. This calibration is
stable as it leans on a more varied data library and can be apparently performed
on the basis of the laboratory spectra as well.
It is important to note that this type of compression is practically lossless at
its reasonably high rates due to the PCA's ability to discard first and foremost
the noise and redundant correlations from the data. It should also be noted that
compression is better for the higher band numbers where the method retains its
robustness and accuracy, our other experiments with hyperspectral land satellite
images show that. The compression rate can be further increased by subsequent
application of a spatial decorrelating techniques such as JPEG or DCT.
In addition to the reduction of the data dimensions PCA can be used for au­
tomatic correction of the impulse noise due to its unique interpolation abilities.
The principal components so obtained are characterized by higher informational
content than the initial spectra and can be directly used for various data in­
terpretation tasks (see, for example, Shkuratov et al. 1996; Smith et al. 1985;
Vasilyev 1996).
Acknowledgments. The author thanks the ADASS VII Organizing Com­
mittee for o#ering him full financial support to attend the Conference.
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