Keywords: Synthetic aperture radar, Subband coding, Block Truncation code, Quadtree decomposition
Abstract This paper proposes a subband synthetic aperture radar (SAR) image coding by using variable block truncation code, which is assisted by quadtree decomposition (QT) technique to divide image data. Quadtree decomposition is a simple technique for ordering an image data to hierarchical levels. This technique is partitioning an image into variable-sized blocks based on a quadtee structure, that the data in each subblock-size will be homogeneous. Quadtree decomposition will optimize a block for coding by setting up variable block sizes. Therefore, memory and process times are reduced when compared with fixed-block truncation code and absolute moment block truncation coding. The subband image coding is based on the decomposition of a signal into narrow band by a set of parallel filters. This paper uses the 16-band separable subband filter based on the quadrature mirror filter (QMF) by using the separable 2-D QMF, which allows the aliasing to be removed in the reconstruction signal. The coefficients are obtained from each subband and encoded by a classified priority, that is the lower subband having more information than the higher subband. It should be coded with a small block size. In this case, we choose the minimum block equal to 1x1 and the maximum block size is 16x16. For the higher subband, we choose 4x4 minimum block and 16x16 maximum block. The lower subband, especially a part of approximation can be coded with the small block size, but a part of details can be coded large block than the approximation. A combination of both techniques improves the minimum mean square error and image quality.
I.Introduction
Block truncation code (BTC) is the simple technique that is firstly introduced by Delp and Mitchell [1,2]. It is an efficient image coding method that has been adapted to obtain the statistical properties of the block in image compression.
This algorithm, the image is firstly divided into non-overlap blocks.
The BTC output data set is including of the binary bit plane, which defines the quantization level of each pixel,
and two-reconstruction level values, determined by the mean and standard deviation of the block
Xi .
Where i=1 to
II , q is the number of pixels with values greater thean or equal to the transmitted mean
u , the two output levels
a and
b from the quantizer for each block are given by
where
is the sample mean and
is the standard deviation that is
In addition, the BTC method is a fixed-based method, that inefficiency for coding. We have the method for dividing an image into varieties of the small block. The pixel in the block is homogeneous called quadtree decomposition (QT) [3,4]. This QT is efficiency than fixed block, especially used for coding SAR image. This paper proposes the combination of subband coding and variable block truncation code.
Section II introduces the subband coding of images. Section III describes the quadtree decomposition method. Section IV describes the combination between the quadtree decomposition method and block truncation code. Simulation result and conclusion are given in section V and VI
II. Subband Image Coding
Subband coding [5] is the most important to obtain high bit-rate compression as illustrate in Fig 1. This figure shows the transform using the two-channel filter bank. The part of the system on the left of the dotted line is the analysis part, and the part of the right is the synthesis part. In the analysis stage, the input data signal is processed by the analysis filter bank consisting of the time-invariant linear with transfer function , , such that is lowpass and is highpass filter respectively.
Figure 1. General two-channel subband coding system
The basic two-channel system in Figure 1 should be designed so that if no compression takes places, the system output will be equal to the translation of the system input. This is called the perfect reconstruction condition or PR-QMF [6,7]. We identify of the two conditions for perfect reconstruction. One condition is removed distortion and the other is removed alising. The signal can be perfectly reconstructed if the analysis and systhesis filters satisfy the conditions (5), (6), (7), (8).
G
0(z)=-H
1(-z) (5)
G
1(z)=-H
0(-z) (6)
H
1(z)=z
-(n-1)H
0(-z
-1)
(7)
H
0(z)H
0(-z
-1)+H
0(-z)
H
0(-z
-1)=1 (8)
III. Quadtree Decomposition
Quadtree Decompostion (QT) [3,4] is the analysis technique that involves subdividing the image into blocks that are more homogeneous than the image itself. This technique works by dividing the square image into four equal-sized squared blocks by determining the criterion and then testing each block to meet same criterion of homogeneity. If 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. The result may have blocks of several different sizes. In the Figure 2 illustrates the result of QT
(a)
br>
(b)
Figure 2. quadtree decomposition. (a) quadtree decompostion an image.
(b) Tree structure of quadtree
The quadtree is the tree structure in which each internal node has four branches emanating form it. In the other words, each node in the quadtree has either four children as illustrated in Figure 3. The four children of a particular parent node represent the four subblocks obtained by splitting the parent block into four equal-sized square blocks. In this case, all of leave nodes are compressed by BTC method, described in the next section.
