ABSTRACT:  SAR image compression is very important in reducing
the costs of data storage and transmission in relatively slow channels.
In this paper, we propose a compression scheme driven by texture analysis,
image segmentation and speckle noise reduction within the wavelet framework.
The result is favourable compared to the conventional zerotree wavelet
compression method.
* Presented at the Fourth International Conference
on Signal Processing ICSP'98, Beijing, China, October 1216, 1998.
1. Introduction
Synthetic aperture radar (SAR) data represents an important source of
information for a large variety of scientists around the world. However,
while the volume of data collected is increasing rapidly, the ability to
transmit it to the ground, or to store it, is not increasing as fast. Also,
while storage densities on archiving media are improving with technological
developments, our ability to generate new data is increasing even faster.
Thus, there is a strong interest in developing data encoding and decoding
algorithms which can obtain higher compression ratios while keeping image
quality to an acceptable level.
There are some special characteristics to SAR imagery which affect
the design of an image compression algorithm. The first is the speckle
phenomena which results from the coherent radiation. A fully developed
speckle pattern appears chaotic and unordered, and severely degrades the
quality of SAR images. The second is that there is rich texture information
and large homogeneous regions in SAR images. This makes it natural to consider
a way to reduce coding bits within homogeneous regions of terrain. The
third is that very high dynamic range of SAR image data is unlike those
of image data from other sensors, such as optical sensors. These differences
mean that encoding/decoding algorithms designed for optical data may not
be appropriate for SAR data.
Wavelet transforms have received significant attention because their
multiresolution decomposition allows efficient image analysis. It has
been used in analysis, noise reduction and data compression of SAR images
[1]. Thus, using the discrete wavelet transform (DWT),
the procedures of terrain segmentation, speckle noise reduction and data
compression can be efficiently combined in a single process of decomposition
and reconstruction. In this work, we will develop an algorithm using treestructured
texture analysis, softthresholding speckle reduction, quadtree homogeneous
decomposition, and modified zerotree coding scheme. The result is compared
to the conventional zerotree wavelet transform scheme and shows that our
method is very promising method for practical use.
2. Texture Analysis
with TreeStructured Wavelet Transform
Using the DWT, every coefficient at a given scale can be related to
a set of coefficients at the next finer scale of similar orientation. The
coefficient at the coarse scale is called the parent, and all coefficients
corresponding to the same spatial location at the next finer scale of similar
orientation are called children. For a given parent, the set of all coefficients
at all finer scales of similar orientation corresponding to the same location
are called descendants.
The traditional pyramidtype wavelet transform recursively decomposed
subsignals in the low frequency channels. However, since the most significant
information of a texture often appears in the middle frequency channels,
further decomposition just in the lower frequency region, such as the conventional
wavelet transform does, may not help much for SAR image which contains
rich texture information. Thus, an appropriate way to perform the wavelet
transform for textures is to detect the significant frequency channels
and then to decompose them further.
Here, we approach this problem by analyzing SAR images by the treestructured
wavelet transform used in [3]. The key point is that
the decomposition is no longer simply applied to the low frequency subsignals
recursively. Instead, it can be applied to the output of any filter h_{LL},
h_{LH}, h_{HL} or h_{HH}. It can be described as
the following:

Decompose a given textured image with 2D two scale wavelet transform
into 4 subimages, which can be viewed as the parent and children nodes
in a tree.

Calculate the energy of each decomposed image (children node). That
is, if the decomposed image is x(m,n), with 1 <=
m <= M and 1 <= n <= N, the energy
is:
e = 1/(MN) SUM(i=1,M) SUM(j=1,N)
x(m,n)(1)

If the energy of a subimage is significantly smaller than others, we
stop the decomposition in this region since it contains less information.
This step can be achieved by comparing the energy with the largest energy
value in the same scale. That is, if e < C e
max, stop decomposing this region where C
is a constant less than 1.

If the energy of a subimage is significantly larger, we apply the above
decomposition procedure to the subimage.
This method is analogous to computing the complete wavelet packet transform
to a certain maximum level, then pruning the branch from top to bottom
using the above energy threshold. The texture factors are created after
this step. It is represented as a series of constants {F1,
F2, ... , Fl, ...}
which corresponds to a series of frequency channels. Fl
is a constant between (0  1). In a frequency channel with more texture,
Fl is smaller; in a channel with less
texture, Fl is larger.
3. Homogeneity Map
An image map which specifies the degree of homogeneity can be helpful
in achieving higher compression gain because we can allocate fewer bits
to homogeneous regions while allocating more bits to those regions containing
more detail and sharp features. Here, we apply a very simple segmentation
scheme based on quadtree decomposition of the image at the lowest scale.
Quadtree decomposition is an analysis technique that involves subdividing
an image into blocks that are more homogeneous than the image itself. It
starts at decomposing the whole image into four equal sized blocks, and
then testing each block to see if it meets some criterion of homogeneity
(e.g. if all the pixels in the block are within a specific dynamic
range). If a block meets the criterion, it is not divided any further.
If it does not meet the criterion, it is subdivided again into four blocks,
and the test criterion is applied to those blocks. This process is repeated
iteratively until each block meets the criterion.
After quadtree decomposition, we get two lists: a homogeneous
list and a target list. The homogeneous list consists of the relatively
homogeneous regions. Each homogeneous region is represented by the coordinates
of the pixel at the left up corner and the size of the region. The target
list consists of those single component regions, represented by their coordinates.
The test criterion we choose is to split a block if the maximum of the
block elements minus the minimum value of the block elements is greater
than the threshold t_{h}.
t_{h }
= g s
_{h}
(2)
where s_{h} is
the standard deviation of the wavelet coefficients at the highest frequency
band in the diagonal direction, and g
is a selected constant.
4. Speckle Reduction
Speckle noise is modeled as multiplicative noise. After logarithmic
transform, the multiplicative noise become additive noise. The discrete
wavelet transform is a linear transform and the speckle noise is still
additive in the wavelet domain. A soft threshold [2]
is applied to all the wavelet coefficients except those of the lowest scale.
This removes some of the speckle inherent in SAR imagery while preserving
much of the detail, thus improving compression performance. The value of
the threshold t_{l}
is given by the formula:
t_{l} =
F_{l} s_{l}
sqrt{ 2 log(n_{l}) }
(3)
where n_{l} is the number of pixels in each
frequency band, s_{l}
is the same as s_{h },
and F_{l} is the feature factor at the corresponding
frequency channel.
5. Modified SPIHT
Coding Scheme
The embedded zerotree coding (EZW) [4] is a very
effective and computationally simple technique for image compression. The
"set partitioning in hierarchical trees'' method (SPIHT) [5]
improves the performance of EZW based on three concepts:

partial ordering of the transformed image elements by magnitude, with
transmission of order by a subset partitioning algorithm that is duplicated
at the decoder,

ordered bit plane transmission of refinement bits, and

exploitation of the selfsimilarity of the image wavelet transform across
different scales.
Here, we modify the SPIHT by softthresholding, homogeneous map, and
feature factors so that it is more appropriate for SAR images.
A wavelet coefficient x is said to be insignificant
with respect to a given threshold T if x
< T. The zerotree structure is based on the hypothesis
that if a wavelet coefficient at a coarse scale is insignificant with respect
to a given threshold T, then all wavelet coefficients of the same
orientation in the same spatial location at finer scales are likely to
be insignificant with respect to T. In the progressive transmission
mode, the nth bit of the wavelet coefficients is transmitted if
2^{n} <= c_{i,j} < 2^{n+1}.
To make clear the relationship between magnitude comparisons and message
bits, we use the following function to indicate the significance of a set
of coordinates t.
S_{n}(t) =
1 if max{ c_{i,j} }
>= 2^{n}, (i,j) Î
t
=
0 otherwise. (4)
Our method is different from the conventional EZW or SPIHT methods in
the following ways:

A different parent may have the same children because the treestructured
wavelet transform allows the size of children to be smaller than that of
the parent, which is unlike the pyramid structure used in the SPIHT method.
For example in Figure 1, the coefficient in the scale
branch (3,2) has descendants in (3,8), (3,9), (3,10), (3,11), (2,8), (2,9),
(2,10), (2,11).

If the descendants have more than one parent, they are regarded as significant
once they satisfy the condition of the threshold Ti from any
one of their parents f; the descendants are insignificant only when they
satisfy the condition of the thresholds { T1,
T2, ... , Ti }
from all of their parents.

The condition of S_{n} is changed to be max{
c_{i,j} } >= F_{l} 2^{n} ,
(i,j) Î t,
where F_{l} is a texture factor. Thus, texture information has
the higher priority in bit allocation.

Two different coding lists, the homogeneous list and target list, are
encoded separately.
6. New Encoding Scheme
Because the homogeneity map of the lowest scale has been created by
the quadtree decomposition, we can reduce the number of bits by encoding
the homogeneity map while allocating more bits to highlighting areas of
greater detail. To further improve the coding efficiency, the softthresholding
is applied before the start of coding at other scales. The residual from
softthresholding and coding is kept and then losslessly compressed using
arithmetic coding and transmitted to decoder based on the users' demand.
The features of the new method are:

Speckle reduction: Soft thresholding is applied to all wavelet
coefficients except the lowest scale ones. After quantization, the length
of significant bits of wavelet coefficients is shortened. The residual
part is kept and transmitted based on user's demands.

Encoding homogeneous map: To the components in the homogeneous
list, we send the decoder the average value, the dynamic range and the
size of the homogeneous region, and then use this average value as the
threshold to decide the significant coefficients at the next finer scale.
Then we compute the difference between the value of every component in
the homogeneous region and the average value. We quantize these differences
and transmit them based on the bit plane.

Treestructured coding: The wavelet coefficients in the
target list are quantized and transmitted based on the algorithm used in
the modified SPIHT algorithm. At every scale branch, three candidate encoding
schemes will be tested: raw data, arithmetic coding, and runlength coding.
The candidate with the best performance is chosen as the encoding scheme
at this scale branch.

Residual coding: Efficient compression of these residuals
is essential to the efficiency of the algorithm as a whole. Because this
part of the coefficients possess a rapidly decaying exponential distribution
with a maximal number of zero coefficients. This skewed distribution makes
arithmetic coding the best choice for lossless compression.
7. Experimental Results
The experimental data we choose is Xband highresolution airborne 1look
SAR image showing part of Bedfordshire in southeast England Figure
2. It displays many of the features that typically appear in airborne
imagery. In our experiments, Daubechies 4 (DB4) wavelet transforms (quadrature
mirror filter pairs) are employed.
The tree structure analysis is illustrated in Figure
1. Three level decomposition happen in three places: the lowest scale
channel, the lower vertical scale channel, and the highest diagonal direction.
The compression result is shown in Figure 3 (0.1 bits/pixel),
Figure 4 (0.2 bits/pixel), and Figure
5 (0.2 bits/pixel) with conventional EZW. From those images, we can
see that this algorithm works well on airborne SAR image and outperforms
the conventional wavelet method.
Figure 1: Treestructured analysis.


Figure 2: Original SAR image.

Figure 3: 0.1 bits/pixel



Figure 4: 0.2 bits/pixel 
Figure 5: 0.2 bits/pixel with EZW 
8. Conclusions
We have presented an algorithm that operates through the combination
of image analysis, speckle reduction, and image compression and accomplishes
embedded coding. It is more effective than the conventional zerotree algorithm.
The performance of this coding scheme can also be improved by choosing
more appropriate image analysis tools, and coding sequence based on the
analysis result.
References

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D. Donoho, "DeNoising by SoftThresholding", IEEE Trans. Information
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T. Chang and C. Kuo, "Texture Analysis and Classification with TreeStructured
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