Mixture of Factor Analyzers (MoFA) Models for the Design and Analysis of SAR Automatic Target Recognition (ATR) Algorithm

We study the problem of target classification from Synthetic Aperture Radar (SAR) imagery. Target classification using SAR imagery is a challenging problem due to large variations of target signature as the target aspect angle changes. Previous work on modeling wide angle SAR imagery has shown that point features, extracted from scattering center locations, result in a high dimensional feature vector that lies on a low dimensional manifold. We propose to use rich probabilistic models for these target manifolds to analyze classification performance as a function of Signal-to-noise ratio (SNR) and Bandwidth. We employ Mixture of Factor Analyzers (MoFA) models to approximate the target manifold locally, and use error bounds for the estimation and analysis of classification error performance. We compare our performance predictions with the empirical performance of practical classifiers using simulated wideband SAR signatures of civilian vehicles.;We then extend this work to design optimal maximally discriminative projections (MDP) for the manifold structured data. An optimization algorithm is proposed that maximizes the Kullback Leibler (KL)-divergence between two mixture models through optimizing the closed-form "Variational Approximation" of the KL-divergence between the MoFA models. We then propose to generalize our MDP dimensionality reduction technique to multi-class using non-linear constrained optimization through minimax quasi-Newton methods. The proposed MDP algorithm is compared to existing dimensionality reduction techniques using simulated Civilian Vehicles datadome dataset and real-world MSTAR data.