International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
  
Wavelet transforms have been suggested as an analysis tool for 
the analysis of SAR images (Barbarossa and Parodi 1995). In 
such a framework the wavelet approach maps high frequency 
features. In this paper. a wavelet approach is proposed that - 
detects and describes texture and pattern (hereafter referred to 
as structural features) in a simple SAR image; simple in the 
sense that the land cover classified only contains two types of 
vegetation. A neural network is then used to classify the image 
based upon six components as measured directly from the SAR 
and those derived by wavelet decomposition. 
2. SAR DATA ANDSITE DESCRIPTION 
SAR data was obtained from the shuttle imaging radar 
experiment C (SIR-C). This SAR has multi-frequency and 
multi-polarization capabilities. Available frequencies were X 
(3.0 cm), C (5.8 cm) and, L (23.5 cm) and obtainable 
polarization combinations were HH, HV, VV and VH with 17 x 
25m pixel resolution. The SAR image in Figure 1 is taken over 
the settlement of Pishan in Pei Shan county located in the 
southwest of Xin Jiang, northwest China. It is juxtaposed 
between the southern edge of the Takilimakan desert and the 
northern extent of the Kulun mountain range. 
  
Figure 1. A community of poplar trees (‘white’ lattice) 
interspersed by bushes (varying colours from cyan 
to turquoisc) and surrounding background located in 
Pishan in Pei Shan county in the south-west of Xin 
Jiang, north-west China. 
The original image was subset to a smaller one with dimensions 
of 224 by 224 pixels with three layers of polarization 
combinations L-HH, L-HV and C-HV. Figure 1 therefore shows 
the radar image as composed of three microwave wavelength 
data, the colours based on different frequencies and 
polarizations. Image display colour were assigned as follows: 
red is the L-band horizontally transmitted, horizontally received, 
L-HH(R): green is the L-band horizontally transmitted, 
vertically received, L-HV(G); and blue is the C-band 
horizontally transmitted and vertically received, C-HV(B). A 
visual interpretation of the image is indicative of a grid. Indeed 
a grid of poplar trees with bushes in-between supplanted the 
original ground cover on the existing alluvial fans. This pattern 
and alignment was constructed so as to provide windbreaks for 
the settlements downwind. The ground coverage is therefore 
fairly simple and internally homogeneous. 
3. FEATURE EXTRACTION AND CLASSIFICATION 
METHODOLOGIES 
The 2D Wavelet Transform 
The discussion begins with the definition of the orthonormal 
wavelet (Chui 1992): let L^ (0, 270) represent the set of all 
measurable functions defined from (0, 2 7t) that satisfy 
2 
i 
2 
Ir (x) dx < ® . It is assumed the functions in L^ (0, 2m) 
0 
are expanded periodically into the real line IR = (- %, * oo), that 
is: f(x) = fx m 2x) are satisfied at each x. Let Y have 
unit length, then 
y/ 
Jk 
(o 2 (2 !x— k) (1) 
Equation 1 is referred to as the orthonormal wavelet. 
Where v. ! is the canonical orthonormal basis of L’(IR), that 
1S 7, e = $ e S and V f € 1^ (IR). so that, 
f(x) = Yo. vs (x) in which: 
ik 
; N2 NI 2 
lim eb Y. X Cor ul.eo 
MILNLM2.N2- j2-M2 k--MI 
The orthonormal wavelet whose rank is j has a degenerate 
matrix from rank 0 to rank j. This nature in the wavelet w(x) 
has the advantage of an improved ability in edge detection in 
digital images — in this case SAR. At the same time, (x) 
can also detect the peak signal at multi-resolution. 
The orthonormal wavelet whose rank is j has a degenerate 
matrix from rank O to rank j. This nature in the wavelet ¥ (x) 
has the advantage of an improved ability in edge detection in 
digital images - in this case SAR. At the same time, 7^ (x) 
can also detect the peak signal at multi-resolution. 
There are a number of ways to accomplish wavelet 
decomposition of a 2-dimensional (2D) digital image. For the 
purposes of this research the Stéphanne Mallat pyramid 
algorithm (Mallat 1989) was adopted as follows: let # represent 
the H, operator (i.e. high pass filter), G represent the G, 
operator (i.e. low pass filter), subscripts r and ¢ represent row 
and column respectively and j is defined as before, then: 
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