Multivariate AR Model based Support Vector Machine for Multispectral Remote Sensing Image Classification

Time series statistical models such as autoregressive moving average (ARMA) were considered useful in describing the texture and contextual information of an remote sensing image. To simplify the computation, we use a two-dimensional (2-D) autoregressive (AR) model instead. In our previous research, the 2-D univariate time series based imaging model was derived mathematically to extract the features for further terrain segmentations. The effectiveness of the model was demonstrated in region segmentation of a multispectral image of the Lake Mulargias region in Italy. Due to the nature of remote sensing images such as SAR (synthetic aperture radar) and TM (Thermal Mapper) which are mostly in multi-spectral image stack format, a 2-D Multivariate Vector AR (ARV) time series model with pixel vectors of multiple elements (i.e. 15 elements in the case of TM+SAR remote sensing) are examined. The 2-D system parameter matrix and white noise error covariance matrix are estimated for further classifications. To compute the time series ARV system parameter matrix and estimate the error covariance matrix efficiently, a new method based on modern numerical analysis is developed by introducing the Schur complement matrix, the QR (orthogonal, upper triangular) matrix and the Cholesky factorizations in the ARV model formulation. As for pixel classification, the powerful Support Vector Machine (SVM) kernel based learning machine is applied in conjunction with the 2-D time series ARV model. The SVM is particularly suitable for the high dimensional vector measurement as the "curse of dimensionality" problem is avoided.