Object Localization in the Presence of Noise

Detection and localization of small objects is crucial in many applications, such as surveillance, microscopy, and astronomy. In many space-based imaging applications, the spatial resolution of the imaging system is not enough to localize a small object (point source). Low signal-to-noise ratio (SNR) increases the difficulty such as when the objects are dim. We can model the noise in several ways and consider two cases in this paper. Noise is modeled as additive spatially invariant Gaussian distributed noise and spatially varying Poisson distributed noise. We assume that we have a coarse estimate for the spatial location of an object in an image and that a 2D symmetric Gaussian function approximates the point spread function of the imaging system and, thus, the gray-level distribution of an object. In this paper, we describe a machine learning method that minimizes a cost function derived from the maximum likelihood estimation of the observed image to determine an object's sub-pixel spatial location and amplitude. We call the proposed method Sub-Pixel Location Estimator for Small Objects (SPLEO). We compare the variance of SPLEO (both spatial location and object amplitude estimates) with the Cramer-Rao lower bound (CRLB).

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