Keywords: Polarimetric, Fuzzy, Neural Network, SAR, Classification
Abstract This paper develops a supervised algorithm by incorporating the polarimetric statistics into a fuzzy dynamic neural network (Chen et al., 1996)(Tzeng and Chen, 1997) using a multilook complete polarimetric information. The method makes use of inherent statistical properties of the polarimetric data and hence the information is fully explored. A set of P-L-C-band images acquired by JPL airsar during the PACRIM'96 campaign were used as test images. Validation and effeteness of the proposed scheme were able to demonstrate the utilization of complete polarimetric information. It has been shown that with complete polarimetric data, the fuzzy neural network has substantially reduced its training time and improved the classification accuracy as well. A Lee polarimetric filter was applied to reduce speckle level while preserving the polarimetric properties and is proven to be useful to improve the classification accuracy. The approach also demonstrates the adaptability and flexibility for high dimensional feature vectors such as the complete polarimetric presented here.
1. Introduction
In classification of SAR image, three linear polarized data (diagonal term of covariance matrix) is often used and a proper classification results could be obtained (Chen, 1996; Tzeng, 1997). As stated in (Lee et al., 2000), there are basically three approaches: 1) algorithms based on image processing techniques, 2) algorithms based on a statistical model, and 3) algorithms based on em wave scattering mechanisms. Approach 1) can be supervised or unsupervised, while 2) and 3) are devised to be supervised only. Supervised and unsupervised algorithms are complementary to each other; each has its own advantages and disadvantages, depending on their purposes and applications. In all image classifications, still only partial polarimetric data are mostly often utilized. Hence, one has not yet taken full advantage of polarimetric data. This certainly does not necessarily mean that partial polarimetric data is not sufficient for the applications cited there. However, it may miss some important information that is embedded in the off-diagonal term of covariance matrix. For this purpose, a neural fuzzy classifier based on Wishart distribution for fully polarimetric SAR is demonstrated in this paper.
2. Polarimetric Sar Image
2.1 Statistical Properties
A polarimetric SAR records the matrix S. A scattering matrix S is a relationship between the incident field and the scattering field
 | (1) |
where the subscripts in S denote the polarized states, and k is incident wavenumber, r the range from radar antenna to target center. With the complex scattering matrix S available, the interactions of radar waves and target medium can be fully described in the sense of complete polarization response. For simplicity, a complex vector v may be defined by elements of S as
 | (2) |
where T denotes the matrix transpose and q the dimension of v, q = 4 for bistatic case and q = 3 for backscatter case by duality theorem stating
Svh==
Shv for a reciprocal medium. SAR is a coherent imager and thus unavoidably suffers from speckle noise. This degrades image quality. Thus, SAR images are usually multi-look processed by averaging several neighboring one-look pixels. For polarimetric SAR system, it requires averaging several one-look covariance matrices
 | (3) |
where vi is i
th look elements vector in Eq. (3), n is number of looks, Z is a Hermitian matrix. The statistics of the Z has a complex Wishart distribution [Lee, 2000)
 |
(4)
(5) |
where C= < Z > denotes the feature covariance matrix and < > the ensemble average.
2.2 Polarimetric Speckle Filter
SAR image records the scattered echoes from the scatterers within the illuminating cell. It causes speckle phenomena. To obtain better classification results, the despeckle procedure is performed before the SAR image is applied for classification. A new despeckle technology proposed and proven well suited for fully polarimetric SAR data [Lee, 1999] is applied in filtering the speckle of the SAR image in this study.
