| This thesis addresses the problem of target detection when the statistical description of the target varies or is not exactly known. We are motivated by terrain classification in polarimetric synthetic aperture radar where land cover signatures vary depending on several factors. To address this problem we construct a representative random process using wavelets that conveys the aggregate scattering properties of each terrain type. The representative process is matched to the original terrain models through the Bhattacharyya coefficient, which serves as a measure of the stochastic distance between the wavelet-based random process and the original processes.; Assuming Gaussianity, the design of the representative process reduces to determining a unitary set of eigenvectors, the associated set of eigenvalues, and the mean vector. The matching algorithm iterates between a migration algorithm that searches for the best basis from a wavelet packet tree and a fixed-point algorithm that determines the optimal eigenvalues. A subsequent fixed-point algorithm determines the optimal mean vector.; We test the matching algorithm on two classes of well-studied random processes, first-order Markov processes and band-limited processes. The algorithm is then used to construct representative processes for terrain classes from POL-SAR images of Canadian boreal forests which are then implemented as terrain signatures in a classification test. The classifier is tested on two different images that have disparate terrain statistics, and the performance is compared with the results generated by several standard classifiers. |
