Object recognition in images degraded by gaussian and photon-limited noise

In this thesis the problem of detecting and localizing an object embedded in a background terrain image is addressed. New algorithms based on the impulse-restoration (IR) approach and Generalized Likelihood Ratio Test (GLRT) detection are formulated and compared to traditional detectors. In IR, the objective is to restore a delta function indicating the object's location. GLRT is an extension to the classical Likelihood Ratio Test (LRT) when the likelihood ratio is parameterized by unknown parameters. Here we develop solutions based on IR and GLRT for images with additive Gaussian noise and photon-limited noise. For the Gaussian noise case, a solution based on IR is proposed. A maximum likelihood (ML) framework is proposed to solve this restoration problem. The expectation-maximization (EM) algorithm is used to find the ML solution. For the photon-limited noise case, a solution based on IR is proposed. A ML and a Bayesian framework are proposed to solve this restoration problem. The EM algorithm and non linear filtering that highlights impulses are used for the ML approach. A new prior that captures the impulsive nature of the desired solution is used for the Bayesian approach. GLRT algorithms are presented for images with Gaussian noise and photon-limited noise. It is shown that the GLRT approach requires estimates for the object location and the background statistics. ML estimates for the object location and the background statistics are derived for the Gaussian noise and photon-limited noise cases. We use a Monte-Carlo study and localization-receiver-operating characteristics (LROC) curves to evaluate the performance of the proposed approaches quantitatively and compare it with existing methods. We present experimental results that demonstrate that IR and GLRT are powerful approaches for detecting known objects in images degraded by noise. For the Gaussian noise case, it is demonstrated that the IR based EM algorithm outperforms the GLRT based algorithm and is the best overall algorithm for detecting and localizing an object in a scene. It is also shown that accurate modeling and estimation of the background and noise statistics are crucial for realizing the full potential of the IR approach. For the photon-limited noise case, it is demonstrated that the GLRT based algorithm outperforms all IR based algorithms introduced. It is also shown that incorporating prior knowledge of the characteristics of the delta function enhances the performance of the IR approach.