Robust Adjusted Likelihood Function for Image Analysis

Model misspecification has been a major concern in practical model based image analysis. The underlying assumptions of generative processes usually can not exactly describe real-world data samples, which renders the maximum likelihood estimation (MLE) and the Bayesian decision methods unreliable. In this work we study a robust adjusted likelihood (RAL) function that can improve image classification performance under misspecified models. The RAL is calculated by raising the conventional likelihood function to a positive power and multiplying it with a scaling factor. Similar to model parameter estimation, these two new RAL parameters, i.e. the power and the scaling factor, are estimated from the training data using minimum error rate method. In two-category classification case, this RAL is equivalent to a linear discriminant function in log-likelihood space. To demonstrate the effectiveness of this RAL, we first simulate a model misspecification scenario, in which two Rayleigh sources are misspecified as Gaussian distributions. The Gaussian parameters and the RAL parameters are estimated accordingly from the training data, and the two RAL parameters are studied separately. The simulation results show that the Bayes decisions based on maximum-RAL yield higher classification accuracy than the decisions based on conventional maximum-likelihood. We further apply the RAL in automatic target recognition (ATR) of SAR images. Two target classes, i.e. t72 and bmp2, from MSTAR SAR target dataset are used in this study. The target signatures are modeled using Gaussian mixture models (GMMs) with five mixtures for each class. Image classification results again demonstrate a clear advantage of the proposed approach.