Hyperspectral Image Compression Using JPEG2000 and Principal ...

IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 4, NO. 2, APRIL 2007 201
Hyperspectral Image Compression Using JPEG2000
and Principal Component Analysis
Qian Du, Member, IEEE, and James E. Fowler, Senior Member, IEEE
Abstract—Principal component analysis (PCA) is deployed in
JPEG2000 to provide spectral decorrelation as well as spectral
dimensionality reduction. The proposed scheme is evaluated in
terms of rate-distortion performance as well as in terms of information
preservation in an anomaly-detection task. Additionally,
the proposed scheme is compared to the common approach
of JPEG2000 coupled with a wavelet transform for spectral
decorrelation. Experimental results reveal that, not only does the
proposed PCA-based coder yield rate-distortion and informationpreservation
performance superior to that of the wavelet-based
coder, the best PCA performance occurs when a reduced number
of PCs are retained and coded. A linear model to estimate the
optimal number of PCs to use in such dimensionality reduction
is proposed.
Index Terms—Hyperspectral data compression, JPEG2000,
principal component analysis (PCA), wavelet transforms.
I. INTRODUCTION
HYPERSPECTRAL images typically possess a high
degree of spectral as well as spatial correlation. As a
consequence, data compression can significantly reduce hyperspectral
data volumes to more manageable size for storage and
communication. Wavelet-based lossy compression techniques
are of particular interest due to their long history of providing
excellent rate-distortion performance for traditional 2-D imagery.
Consequently, a number of prominent 2-D compression
algorithms have been extended to 3-D; these 3-D waveletbased
techniques include 3D-SPIHT, 3D-SPECK, and 3-D tarp
(see [1] for a review). In addition, the JPEG2000 standard has
been widely applied to 3-D hyperspectral image coding (e.g.,
[2]–[4]) owing to its ability to code multiple image components.
However, it has been argued that such a direct extension from
2-D to 3-D, without the consideration of special characteristics
of hyperspectral imagery, may be problematic [5], as data
analysis applied subsequent to compression may be affected.
Typically, the development of a 3-D compression algorithm
involves coupling a decorrelating transform in the spectral
direction with a spatial wavelet transform plus a coding algorithm
suitably modified for a 3-D data array. Most often,
a wavelet transform is also deployed spectrally, so as to implement
a 3-D wavelet decomposition. Indeed, Annex I of
Part 2 of the JPEG2000 standard supports a spectral discrete
wavelet transform (DWT) in this manner, and it has been shown
that JPEG2000 plus a spectral DWT generally achieves ratedistortion
performance superior to that of other wavelet-based
Manuscript received June 29, 2006; revised October 8, 2006.
The authors are with the Department of Electrical and Computer Engineering,
GeoResources Institute (GRI)—Mississippi State HPC 2 , Mississippi State
University, Mississippi State, MS 39762 USA (e-mail: du@ece.msstate.edu;
fowler@ece.msstate.edu).
Digital Object Identifier 10.1109/LGRS.2006.888109
Fig. 1. Rate-distortion performance for PCA + JPEG2000 using all principal
components (P = 224) compared to that of DWT + JPEG2000. Rate is
expressed in terms of bits per pixel per band. Distortion is measured as the
signal-to-noise ratio (SNR), being the log ratio of signal variance to meansquare
error, as in [1].
TABLE I
SNR (IN DECIBELS) AT 1.0 bpppb
Fig. 2. SNR performance as the number of principal components coded P
varies for PCA + JPEG2000 on the Jasper Ridge dataset.
techniques [1]. However, Annex I supports other transform
structures as well, including arbitrary transforms in the form
of unitary-matrix decompositions.
1545-598X/$25.00 © 2007 IEEE

202 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 4, NO. 2, APRIL 2007
TABLE II
NUMBER OF PCS P ∗ THAT YIELDS MAXIMUM SNR
In this letter, we investigate the performance of principal
component analysis (PCA) for spectral decorrelation in conjunction
with JPEG2000 coding. This letter has four primary
objectives. First, we compare this PCA-based spectral decorrelation
to the more common approach of a DWT spectral
transform. Second, we investigate the impact of using PCA for
dimensionality reduction in addition to spectral decorrelation,
observing the effect that the number of principal components
(PCs) used in compression has on rate-distortion performance.
Third, we evaluate the performance of JPEG2000 with PCAbased
spectral decorrelation in terms of information preservation,
i.e., in terms of the usefulness of the reconstructed data
in analysis, such as detection and classification. Finally, using
our observations of both rate-distortion as well as data-analysis
performance, we develop a heuristic that estimates the optimal
number of PCs to be retained during dimensionality reduction.
Our experiments indicate that, not only does PCA outperform
the DWT for spectral decorrelation, the best performance occurs
when only a small subset of PCs is coded instead of the
entire set. The simple linear heuristic we develop estimates the
optimal number of PCs, from both the rate-distortion as well as
information-preservation perspectives.
II. JPEG2000 AND PCA-BASED
SPECTRAL DECORRELATION
A. Implementation
PCA, a well-known technique in multivariate data analysis,
has been widely used in the hyperspectral setting for spectral
decorrelation as well as spectral dimensionality reduction. Capable
of optimal decorrelation in a statistical sense, PCA often
provides excellent decorrelation in practice. When all PCs are
retained, PCA is commonly known as the Karhunen–Loève
transform (KLT), in which case a hyperspectral image with
N spectral bands produces an N × N unitary KLT transform
matrix. As this matrix is data dependent, it must be communicated
to the decoder in any KLT-based compression system.
Alternatively, PCA can effectuate dimensionality reduction by
retaining in the KLT transform matrix only those eigenvectors
corresponding to the P largest eigenvectors. The data volume
passed to the encoder then has P

DU AND FOWLER: HYPERSPECTRAL IMAGE COMPRESSION USING JPEG2000 AND PCA 203
TABLE III
DETECTION PERFORMANCE OF PCA + JPEG2000 AND DWT + JPEG2000
standard. For both PCA + JPEG2000 and DWT + JPEG2000,
a spatial 9/7 transform with five levels is used.
Fig. 1 shows rate-distortion performance when using PCA +
JPEG2000 and DWT + JPEG2000 to encode the three AVIRIS
scenes. Table I tabulates the SNR for PCA + JPEG2000 and
DWT + JPEG2000 at a fixed rate; also shown is the performance
when JPEG2000 is used with no spectral decorrelation.
We see that, in all cases, although DWT-based spectral decorrelation
improves SNR by around 15 dB with respect to no
spectral decorrelation, PCA-based spectral decorrelation results
in a further 5-dB increase. From a statistical perspective, PCA
offers optimal decorrelation while highly structured correlation
is known to exist between DWT coefficients, both within
subbands and across subbands. While JPEG2000 exploits this
DWT correlation structure spatially, no attempt is made to
exploit residual correlation across components, i.e., spectrally.
As a consequence, a spectral DWT leaves a significant degree of
correlation present in the spectral direction; the spectral PCA,
with its optimal decorrelation, thus performs better.
III. JPEG2000 AND PCA-BASED
DIMENSIONALITY REDUCTION
A. Rate-Distortion Considerations
In the use of PCA above, we retained and coded the full
number of PCs. Theoretically, PCRD optimization results in an
optimal rate allocation and SNR, thereby obviating the need for
explicit dimensionality reduction. In theory, one should code
all PCs and let the PCRD optimization allocate rate across the
PCs, as PCs that are unneeded will be automatically allocated
zero rate. However, in practice, rate-distortion performance
is improved if fewer than the full complement of PCs is
coded (i.e., for P

204 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 4, NO. 2, APRIL 2007
Fig. 4. ROC curves for the Moffett dataset at 0.05 bpppb. P d =
probability of detection. P f = probability of false alarm.
in the data. In this letter, unsupervised detection is considered.
We focus on anomaly detection, wherein an anomaly is defined
as a small object or material whose spectral signature is very
different from the background. In hyperspectral applications,
such an anomaly is most likely an unknown target. Anomaly
detection provides a good test of the performance of lossy
compression in information preservation because these small
objects or materials are prone to be sacrificed during compression,
although they may be, in fact, quite important to the
hyperspectral application.
The well-known RX algorithm is employed for anomaly
detection [7]. Since there is no real ground truth available, we
consider the detection map resulting from the original data to be
ground truth; the detection map resulting from the reconstructed
data is then compared to it. The measure of similarity comparison
is the spatial correlation coefficient ρ—the closer ρ is to
1.0, the better the detection performance is considered to be.
Fig. 3 indicates that the detection performance varies with
P , which is the number of PCs used for compression, with the
maximal correlation coefficient occurring in all cases for fewer
than 224 PCs. Once again, this experiment demonstrates that
it is unnecessary, even undesirable, to retain the minor PCs,
since they contain noise only and will not contribute to target
detection.
Table III presents P † , which is the number of PCs that
achieves maximum detection performance, for each of the
three AVIRIS datasets. Additionally, detection performance
for PCA + JPEG2000 using all 224 PCs as well as the
performance for DWT + JPEG2000 is given. We see that, in all
cases, the maximum ρ occurs for strictly fewer than 224 PCs;
additionally, this maximal PCA + JPEG2000 ρ is greater than
that of DWT + JPEG2000 in all cases.
Table III also examines the effect that compression has
on anomalous pixels as measured using the Spectral Angle
Mapper (SAM); such anomalous pixels typically are among
the worst for spectral distortion in the dataset. In general, PCA
+ JPEG2000 using all the PCs results in less spectral distortion
than DWT + JPEG2000 for the anomalous pixels. Table III
also shows the mean and standard deviation of the SAM over
the entire image, and from these values, we observe that the
average spectral distortion is typically quite small, even for low
rate. On average, DWT + JPEG2000 incurs the most average
Fig. 5. P ∗ and ˜P ∗ versus rate R.
TABLE IV
COMPARISON BETWEEN P ∗ AND ˜P ∗ AND THE RESULTING SNRS
spectral distortion, while PCA + JPEG2000 using P † PCs
incurs the least.
In comparing Table II with Table III, it is interesting to see
that P ∗ , which is the number of PCs yielding maximal SNR
in Table II, is typically close to P † , which is the number of
PCs yielding maximal detection performance in Table III.
Often, these two values are identical. Consequently, we argue
that, if we code the dataset using P ∗ PCs, we can use the
reconstructed image for practical data analysis, such as target
detection, because this same number of PCs should provide
good performance in that sense as well. We use this observation
as a motivation for developing a heuristic that estimates P ∗ in
Section III-C.
In order to further evaluate the detection performance,
analysis of the receiver operating characteristic (ROC) is
conducted. Target pixels are defined by thresholding the
detection map produced from the original data with a threshold
of half the maximum. Detection maps from the reconstructed
data are then thresholded with thresholds ranging from 10%
to 90% of maximum, and the detection and false-alarm
probabilities are calculated for each threshold using the
previously defined target pixels. Fig. 4 shows the resulting
ROC curves for the Moffett dataset, which has a sufficient
number of anomalous pixels for meaningful ROC analysis.
To quantify the performance, the areas under the ROC curves
are given in Table III for Moffett, with a larger area indicating

DU AND FOWLER: HYPERSPECTRAL IMAGE COMPRESSION USING JPEG2000 AND PCA 205
TABLE V
RATE-DISTORTION AND ANOMALY-DETECTION PERFORMANCE
superior detection performance. We see that the ROC areas
generally match the correlation coefficients in Table III.
C. Linear Model for Dimensionality Reduction
Let P ∗ be the number of PCs that yields maximal SNR for
a given dataset. From Fig. 2, P ∗ clearly varies with the rate
R of the coding. We thus propose a simple linear model on
R as an estimate of P ∗ . This is illustrated in Fig. 5 in which
wefitalinetotheP ∗ versus R curves for the three AVIRIS
datasets; specifically, we estimate P ∗ as ˜P ∗ = αR + β, where
α =87.7778 and β =16.2222 are constants. Even though the
P ∗ versus R curves are rather nonlinear in Fig. 5, this linear
model fits the curves quite closely at the lower rates, which is
crucial, since, from Fig. 2, the performance suffers the most
from not coding at P ∗ when the rate is low.
As shown in Table IV, this linear model yields rather accurate
results in some cases. For instance, when the bit rate is
0.25 bpppb, the estimated ˜P ∗ values are very close to the true
P ∗ values. In some cases, however, ˜P ∗ can be quite different
from P ∗ . For instance, the Cuprite scene yields the P ∗ versus
R curve furthest from the linear model, as shown in Fig. 5; at
0.5 bpppb, the model gives ˜P ∗ =75, while P ∗ =57for this
dataset. Fortunately, the difference in SNR between these two
values is only about 0.05 dB, which is relatively negligible. As
a consequence, we conclude that the model provides a simple
yet effective estimate of P ∗ .
To further evaluate the proposed linear model, Table V
summarizes the SNR and ρ values resulting from using P ∗
(maximum SNR), P † (maximum ρ), and ˜P ∗ from the linear
model. In many cases, P ∗ is close to P † ; in other cases, these
two numbers are different, but the resulting performance is still
close. Most importantly, ˜P ∗ , from the linear model, always
yields comparable SNR and ρ.
IV. CONCLUSION
In this letter, we investigated the performance of spectral
PCA in conjunction with JPEG2000 for hyperspectral image
compression, comparing to the common approach of a spectral
DWT followed by JPEG2000. Experimental results on AVIRIS
datasets yield the following observations: 1) spectral decorrelation
via PCA results in rate-distortion performance superior
to that of a spectral DWT; 2) rate-distortion performance is
further improved by retaining and coding only a subset of PCs
rather than using all the PCs; 3) data-analysis performance,
such as anomaly detection, is similarly maximized by coding
a subset of PCs rather than all the PCs; 4) the number of
PCs that yields maximum SNR for a given dataset is usually
close to the number of PCs that yields maximum detection
performance; and 5) a simple linear model can effectively
estimate the optimal number of PCs. Consequently, we conclude
that the capabilities of PCA for decorrelation simultaneous
with dimensionality reduction offer the potential for an
excellent data-compression performance, significantly superior
to that obtained by other techniques based on 3-D wavelet
transforms.
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