Journal of Computer and Communications, 2014, 2, 31-36
Published Online January 2014 (
An Improved EZW Hyperspectral Image Compression
Kai-Jen Cheng*, Jeffrey C. Dill*
School of Electrical Engineering and Computer Science, Ohio University, Athens, USA.
Email: *;
Received October 2013
The paper describes an efficient lossy and lossless three dimensional (3D) image compression of hyperspectral
images. The method adopts the 3D spatial-spectral hybrid transform and the proposed transform-based coder.
The hybrid transforms are that Karhunen -Loève Transform (KLT) which decorrelates spectral data of a hy-
perspectral image, and the integer Discrete Wavelet Transform (DWT) which is applied to the spatial data and
produces decorrelated wavelet coefficients. Our simpler transform-based coder is inspired by Shapiro’s EZW
algorithm, but encodes residual values and only implements dominant pass incorporating six symbols. The pro-
posed method will be examined on AVIRIS images and evaluated using compression ratio for both lossless and
lossy compression, and signal to noise ratio (SNR) for lossy compression. Experimental results show that the
proposed image compression not only is more efficient but also has better compression ratio.
Wavelet Transform; Karhunen-Loève Transform; Transform-based Image Compression;
AVIRIS Hyperspectral Image; Embedded Zerotree Wavelet
1. Introduction
Hyperspectral images are widelyused in various fields
such as agriculture, topography, meteorology and mili-
tary, since they can provide more accurate and detailed
spectral information than other images. NASA Jet Pro-
pulsion Laboratory developed Airborne Visible/Infrared
Imaging Spectrometer (AVIRIS) to produce the 614 pix-
el × 512 line hyperspectral images in 224 contiguous
spectral bands with wavelengths from 400 to 2500 na-
nometers (nm) [1]. The spectrometer generates huge
amounts of data and causes that distribution facilities
cannot economically handle this level of data. It is im-
perative to perform compression.
One popular and widely used image compression is
transform-based compression which successful incorpo-
rates the useful statistical properties of transform for im-
age compression such as energy compaction and decor-
related components. Examples of transforms include the
Karhunen-Loève Transform (KLT), Discrete Fourier
Transform (DFT), Discrete Cosine Transform (DCT) and
Discrete Wavelet Transform (DWT). In general, the
standard image compression, Joint Photographic Experts
Group (JPEG), uses 8 x 8 DCT and the later JPEG2000
uses 2D DWT. Penna et al. [2] compressed hyperspectral
images using JPEG2000 and investigated the perfor-
mance under different transform techniques including
WT, DCT, KLT, and various combinations.
Shapiro [3] proposed the classic embedded zerotree
coding (EZW) using wavelet transform to compress im-
ages. Bilgin et al proposed three-dimensional (3D) image
compression algorithm [4].The 3D-SPIHT was proposed
by Kim and Pearlman [5]. Sohn and Lee [6] successfully
applied the 3D-SPIHT algorithm with symmetrical 3D-
DWT to hyperspectral images.
The proposed image compression utilizes the 3D
space-spectral: The Karhunen-Loève Transform (KLT) is
first applied to remove the correlations among the 224
contiguous highly correlated spectral bands. 2D-Discrete
Wavelet Transform (DWT) is applied to remove the spa-
tial redundancies. After the hybrid transform, the mod-
ified EZW algorithm is applied to encode the trans-
formed hyper spectral images. The modifications include
defining a new tree structure, only running the dominant
pass using six symbols and coding residual values. Fig-
ure 1 shows a block diagram of the transform-base- di-
mage compression. The remainder of the paper is orga-
nized as follows: Section 2 describes the integer KLT.
Section 3 discusses the 2D integer DWT. In Section 4,
the modified EZW algorithm for hyperspectral images is
introduced. The last three sections describe the testing of
*Corresponding author.
An Improved EZW Hyperspectral Image Compression
Figure 1. System diagram.
the algorithms using AVIRIS hyperspectral images; pro-
vide results for this proposed hyperspectral image com-
pression and conclusions.
2. Integer Karhunen-Loève Transform
The Karhunen-Loève Transform (KLT) is the data de-
pendent and optimal linear orthogonal transform because
of the eigenvectors matrix derived from the covariance
matrix of the data.
The pixel vector at the ℎ band is expressed as
[, ,,]
ii iiM
A aaa= …………
in the spatial dimension
(x-y plane). If the spatial dimension has m rows and n
columns, the length of the vector is equal to
.M mn= ×
The number of is same as the hyperspectral bands N,
namely i = 1…N. Figure 2 demonstrates the perspective
of the pixel vector in the hyperspectral image.
The covariance matrix is derived from the pixel vec-
tors as follows:
C EAaAa= −−
where E{} is the expected value of the argument, T is
matrix transpose and the
is defined as the mean value
of , as in
a aM
Since the covariance matrix is a real and symmetric
× square matrix, the eigenvectors and eigenvalues
for this matrix can be found [7].
In general, once eigenvectors are found from the cova-
riance matrix, the next step is to order them by eigenva-
lues, highest to lowest. This gives you the components in
order of significance. If applying the ordered eigenve c-
tors to the image, two important features are presented in
the spectral dimensions and they are the decorrelated
spectral data, and the energy compaction. Figure 3 de-
picts the energy compaction in the spectral dimension.
The optimal energy distribution declines monotonically
from the first band to the bottom. After KLT, we call
these bands KLT bands. IKLT bands mean that integer
KLT (IKLT) is implemented by mapping integers to in-
tegers as described below.
In order to attain lossless compression, the reversible
integer KLT is utilized because it is able to map integers
to integers. Based on matrix factorizations [8], the non-
singular eigenvectors of the KLT is factorized as A =
Figure 2. The perspective of the pixel vector in the hyper-
spectral image.
Figure 3. Energy compaction in spectral dimensions.
PLUS where L and S are lower Triangular Elementary
Reversible Matrices (TERM), U is upper TERM, and P
is a reversible permutation matrix. P defines the row in-
terchanges to guarantee diagonal elements that are not
zero. The transformation can be implemented by the lift-
ing scheme, which includes operations of multiplication,
addition and rounding up.
These factorized matrices must be recorded as over-
head information for the reverse transform. Even if not
compressed, representing these matrices as 32-bit float-
ing point numbers computes an overhead of about 0.11
bpppbs for the 224 × 224 matrices. In the experiment
section, we include the overhead into the lossless results
in each table. Figure 3 describes that the integer KLT is
optimal transform in terms of optimal energy compaction
and best decorrelation.
3. 2D-Wavelet Transform
Instead of implementing the 3D discrete wavelet trans-
form (DWT), the following step is to transform the im-
age in the spatial dimension by the use of 2D DWT. The
optimal implementation of the 2D-DWT is the lifting
scheme. It not only has less computational complexity,
but also realizes a reversible integer wavelet transform
In our experiments, the 3D hyperspectral image was
decomposed by the 2D dyadic wavelet Band by Band,
separately. Figure 4 depicts the perspective of the second
An Improved EZW Hyperspectral Image Compression
Figure 4. 2-D wavelet transform coefficients are stored in a
data cube.
level decomposition on each band.
The DWT has two important properties which are
critical for image compression:
1) Energy packing: When an image is wavelet trans-
formed, the transformed image has energy compaction in
spectral dimensions, that is, the wavelet coefficients in
the higher level subbands will, on average, be larger than
those in the lower level subbands.
2) Self-similarity: A wavelet coefficient at a higher
level subband and all wavelet coefficients of the same
spatial orientation at lower level subbands have certain
predictable relationships.
4. Shapiro’s EZW Algorithm
Shapiro invented his Embedded Zerostree Wavelet
(EZW) algorithm taking advantage of the wavelet trans-
form [2]. The EZW algorithm implements a progressive,
embedded image coding method based on the zerotrees
of data structure. All currently significant bits at the same
bitplane together and recursively encodes other pixels for
the next significant bitplane until reaching the least sig-
nificant bitplane. As a result, the lower significant bits
are embedded behind the higher significant bits, so that a
decoder quickly displays a low quality image and better
quality as more bits are received.
We notethree crucial components that make Shapiro’s
EZW algorithm effectivein image compression. First,
due to energy packing, these wavelet coefficients in
higher level subbands could be scanned earlier than oth-
ers in low level subbands. In other words, larger coeffi-
cients will be encoded first. In addition, both receiver and
transmitter know what scanning order is selected such
that it does not include the scanning order in the over-
head. Scanning order used in this paper is Morton scan.
Second, the quad-tree is the fundamental idea of the
EZW algorithm to interpolate the relations among wave-
let coefficients in different subbands; therefore, it is set
up based on the self-similarity. The definition of the
quad-tree was introduced in [2].
There are two steps to complete EZW algorithm: the-
dominant pass and the subordinate pass. The dominant
pass keeps track of the search for significant coefficients
by labeling each pixel among these four labels: signific-
ance positive symbol (POS), significant negative symbol
(NEG), zerotree root (ZTR) and isolated zeros (IZ) in
Figures 5(a)-(c). The subordinate pass quantizes each
significant coefficient that has been found in the domi-
nant pass.
The definitions of four symbols are described below. If
a root coefficient, in absolute value, is larger than a thre-
shold, it is labeled as significant positive (POS) or sig-
nificant negative (NEG) in Figure 5(b). It implies that
some of the coefficients’ descendants are significant. An
isolated zero (IZ) is a root coefficient that is insignificant
but has some significant descendants in Figure 5(c). If
the coefficient is zerotree root (ZTR), it means the root
coefficient itself and its descendants are all insignificant
such that these descendants don’t have to be encoded in
the current iteration in Figure 5(a) .
5. Modified EZW Algorithm
We propose some modifications to simplify the conven-
tion EZW algorithm and improved the compression re-
sults. [10-13] have studied the asymmetrical 3D-DWT
decomposition that causes the asymmetrical statistics of
the transformed hyperspectral image; thus the asymme-
trical tree structure is more suitable for describing the
transformed hyperspectral image. In this paper, the 3D
asymmetric tree structure was designed according to the
properties of hybrid transforms. In Figure 4, a wavelet
coefficient at a higher subband is not only relative to all
wavelet coefficients of the same spatial orientation at
lower subbands at the same band but also in the neighbor
band. Therefore, if the approximation subband is
with -level decomposition at the
first band, while the spatial dimensions of the image are
m-by-n. Any root
( )
, ,0xy
in the approximation has
four immediate children at
(/ 2,,0)
xm y+
(,/2 ,0),(/2 ,/2,0)
l ll
xymxmym+ ++
( )
, ,1xy
In addition, except ones in the approximation, any root (x,
y, 0) at the first band has four children located at the
same spatial orientations (2x, 2y, 0), (2x + 1, 2y, 0), (2x,
2y + 1, 0), and (2x + 1, 2y + 1, 0) on the first band and
one more child (x, y, 1) below it. Note that any pixel not
in the first band has only one child below it. The new tree
structure will continue to branch until no offspring can be
found. The new and simple definition of tree structure is
demonstrated in Figure 6. Each pixel in the low-pass
(approximation) section of band 1 is a tree root.
In addition to the four labels defined in Shapiro’s
EZW algorithm, in this study, we define two more labels,
called positive and negative ZTR (PZT and NZT) in
Figure 5(d). According to [14], they are degree-1 zero-
trees since every coefficient except the root coefficient is
all zeros. Roots of PZT and NZT are positive and nega-
An Improved EZW Hyperspectral Image Compression
Figure 5. Explanation of (a) ZRT (b) POS/NEG (c) IZ and
(d) PZT/NZT.
Bnad1Bnad2Bnad3Band M
Figure 6. A new tree structure: The root has three children
at the same band and one child at the lower band.
tive significant, respectively. A higher degree zero tree
coder generates a shorter symbol stream.
Table 1 shows the coding results of tree (b) and (d) in
Figure 5. Any significant coefficient should do further
search on its child nodes such that there are eight more
symbols generated for each POS/NEG symbol. If applied
to the new PZT/NZT symbols, some redundant symbols
for coding tree (d) can be replaced by one PZT symbol,
which saves an extra eight symbols. This is the main ad-
vantage of adding extra symbols (PZT/NZT).
Table 2 demonstrates that the conventional EZW al-
gorithm encodes the image, Jasper, with and without
PZR/NZT. Their performances are studied in terms of the
total numbers of outputs. Basically, the PZR/NZR is
Table 1. Examples of coded symbols generated by EZW
algorithm for tree (b) and (d).
tree (b)
tree (d) POS,
Coding tree (d) PZT
Table 2. Numbers of coded symbols from the conventional
EZW algorithm with PZR/NZT and without PZR/NZT,
using the bior-4.4 filter on Jasper.
Number of
symbols EZW with
PZR/NZT EZW without
Num of ZRT 9,265,805 10,584,445
Num of PZR 1633198 NA
Num of NZR 1585476 NA
Num of POS/NEG 278442 3497116
Num of IZ 1505055 1505055
parts of the POS/NEG symbols. The total number of
PZR/NZR and POS/NEG should be equal to that of the
POS/NEG from the EZW algorithm without PZR/NZT,
that is, 1633198 + 1585476 + 278442 = 3497116 in Ta-
ble 2. Compared with the numbers of ZRT symbol, add-
ing extra symbols help to reduce 1,318,640 ZRT symbols
in Table 2. Overall, the total symbols are reduced and
the result in better compression ratios.
Moreover, in Shapiro’s EZW algorithm, if a coeffi-
cient is recognized as a significant pixel, the coefficient
will be sent to the subordinate list and set to 0. Table 3
lists the bits rates generated from the dominant and sub-
ordinate passes and shows that the subordinate pass con-
tributes on average one-third of the total bit rate. In order
to improve the compression ratio, we consider removing
the subordinate list such that the significant coefficient is
replaced by a residual value.
(,,) (,,)
RxyzIxyz T= −
where :
( )
is residual value at (x, y, z)
is threshold at the
is absolute value of a pixel at (x, y, z)
This is a simple way to replace the subordinate list, but
still complete the job of quantizing coefficients. In sum,
the outputs of the modified EZW algorithm only have the
symbols stream that contains a sequence of symbols
(POS, NEG, ZTR, PZT, NZT and IZ). At this point, the
proposed method we call is the residual EZW algorithm
incorporating with the PZT/NZT symbols and the new
tree structure.
All 0s
(a) (b)
(c) (d)
All 0s
An Improved EZW Hyperspectral Image Compression
Table 3. Comparison of the bit rates generated by the con-
ventional EZW algorithm using new 3D asymmetric trees
and the hybrid transform.
Compression performance (bpppbs)
Jasper Moffett Low Altitude
Dominant pass 4.23 4.16 4.26
Subordinate pass 1.64 1.48 1.62
Total bit rate 5.87 5.64 5.88
6. Experimental Results
The residual EZW algorithm compresses the first scene
of AVIRIS images, Moffett 01, Jasper 01 and Low Alti-
tude 01. The size of each image is 256 x 256 x 224 and is
stored as 16 bits signed integers. Compression ratio is the
bit per pixel per band (bpppb). The rate-distortion per-
formance is expressed as the signal to noise ratio (SNR)
for various bit rates. The definition of SNR is the average
squared value of the original AVIRIS images is divided
by the mean squared error (MSE).
First, Table 4 demonstrates the lossless performance
of the residual EZW algorithm along with various wave-
let filters. They are Daubechies wavelets (dbN), Symlets
(symN), and Biorthogonal wavelets (biorNr. Nd), which
can be found in the Matlab wavelet toolbox. As a result,
there is no the optimal wavelet filter for all test images.
General speaking, the biorthogonal wavelets are more
suitable for compressing images because of the perfect
symmetry and linear phase.
Second, the lossy performance of the selected conven-
tional technique (3D-SPIHT and 3D-EZW) is compared
to the proposed method. Both methods are based on the
symmetrical 3D-DWT and 3D quad-tree. For lossy com-
pression, the transform-based coder can be stopped at a
predetermined threshold or when the bit budget is
reached. Table 5 to Table 7 show all results (bpppbvs
SNR) of the lossless, and lossy compression based on
predetermined thresholds. All images are decomposed by
4-level bior 4.4 filters, which have better performance for
lossy compression. The results show that the proposed
EZW algorithm outperforms two conventional methods.
Tables 5 and 7 shows that the proposed method consis-
tently has lower compression ratios and relative high
We demonstrate the complexity in terms of simulation
time s (s) on a workstation with Intel(R) Core i5 CPU
2.67 GHz processor and Windows 7 operating system.
All algorithms, compressing the hyperspectral images,
are implemented in MATLAB. Table 8 shows that our
proposed EZW using 6 symbols has a moderate compu-
tational complexity and achieves an improved compres-
sion ratio. Therefore, the residual EZW algorithm is an
efficient lossy and lossless compression algorithm for
hyperspectral images.
Table 4. Lossless compression results (bpppbs) of the resi-
dual EZW algorithm with PZT/NZT using new 3D asym-
metric trees and hybrid transform.
Wavelet Compression performance (bpppb)
Jasper Moffett Low Altitude
Db 2 5.57 5.42 5.72
Db 6 6.59 6.48 6.66
Sym 4 5.49 5.34 5.63
Sym 6 6.53 6.44 6.56
Bior 3.5 5.58 5.41 5.74
Bior 1.3 5.38 5.22 5.53
Bior 1.5 5.40 5.24 5.55
Bior 4.4 5.47 5.29 5.56
Bior 2.4 5.34 5.17 5.49
Bior 2.6 5.33 5.16 5.48
Table 5. Rate distortion (bpppb vs SNR) of various tech-
niques for Moffett 01.
Cutoff Algorithm
Moffett 01
0 1 2 4 8
3D-EZW 7.91 6.51 5.01 3.579 2.41
3D-SPIHT 6.38 5.30 4.15 2.97 1.95
SNR(dB) NA 51.06 48.25 44.09 39.10
Residual -EZW 5.47 3.94 2.53 1.36 0.55
SNR(dB) NA 55.00 52.69 49.71 47.02
Table 6 Rate distortion (bpppb vs SNR) of various tech-
niques for Jasper 01.
Cutoff Algorithm
Jasper 01
0 1 2 4 8
3D-EZW 8.02 6.61 5.13 3.70 2.53
3D-SPIHT 6.42 5.34 4.19 3.01 2.01
SNR(dB) NA 54.21 51.42 47.29 42.28
Residual -EZW 5.29 4.11 2.71 1.47 0.70
SNR(dB) NA 57.23 54.92 51.83 48.53
Table 7. Rate distortion (bpppb vs SNR) of various tech-
niques for Jasper 01.
Cutoff Algorithm
Low Altitude 01
0 1 2 4 8
3D-EZW 8.28 6.87 5.29 3.76 2.42
3D-SPIHT 6.57 5.50 4.38 3.19 2.08
SNR(dB) NA 54.37 51.50 47.17 42.12
Residual -EZW 5.56 4.26 2.86 1.53 0.66
SNR(dB) 0 54.78 52.24 48.87 45.82
An Improved EZW Hyperspectral Image Compression
Table 8. Compare the simulation time in second of various
techniques for hyperspectral images.
Time(s) Jasper 01 Moffett 01
3D EZW 145.49 146.29
3DSPIHT 116.89 120.85
Residual -EZW 66.58 64.64
7. Conclusions
In this paper, we propose a novel transform-based algo-
rithm for lossy and lossless hyperspectral image com-
pression. The introduction of modifications in the resi-
dual EZW algorithm results in higher compression ratios
and moderate computational complexity. Therefore, it is
an efficient image compression for hyperspectral images.
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