Sub-Pixel Localization of Objects Using Multiple Spectral Bands

Most satellite images have adequate spatial resolution and signal-to-noise ratio (SNR) for the detection and localization of common large objects, such as buildings, roads, or bridges in that these objects are described by many pixels that have relatively high SNR. In other applications one wants to be able to localize the position of a single object or closely-spaced objects (CSOs) that are described by only a few pixels (or less than one pixel) with low SNR. In this paper, we describe a method that uses images from multiple spectral bands to increase the accuracy of sub-pixel localization. We assume that the gray level of a pixel is described by a spreading matrix determined by the point spread function of the sensing system. We also assume that we know the approximate location of the observed object or objects in a co-spatially registered 2D neighborhood of each spectral frame. For our experiments we have two spectral bands. We describe a method to estimate the object or objects amplitudes and spatial locations with sub-pixel accuracy using non-linear optimization and information from two spectral bands. We show that our proposed method achieves a higher sub-pixel resolution compared to existing approaches. At a medium SNR (10 dB), we can localize a single object with an error of 0.08 pixels and localize two objects that are separated by 0.7 pixels with an error of 0.11 pixels. We derive the Cramer-Rao Lower Bound and compare the proposed estimator's variance with this bound.