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16 November 2000 Two-dimensional phase gradient autofocus
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High-resolution synthetic aperture radar (SAR) images can be blurred by phase perturbations induced by uncompensated sensor motion and/or unknown propagation effects caused by inhomogeneities in the atmosphere, troposphere, or ionosphere. The inability of the sensor platform to compensate for these effects has driven the development of SAR autofocus algorithms, which are a particular class of blind restoration algorithms. Phase Gradient Autofocus (PGA) was the first robust non- parametric phase estimation and correction algorithm. It has been an enabling technology for high-resolution SARs and is currently being used in a number of operational SAR systems. Most phase errors experienced by SARs defocus the image in one dimension. However, some proposed systems, such as satellite-based UWB foliage penetration (FOPEN) systems will suffer from potentially severe propagation effects through the ionosphere, including Faraday rotation, dispersion, and scintillation. These effects would cause defocus coupled in range and cross-range, degrading the SAR image by a non-separable 2D phase error. In this work, we present the 2D formulation of PGA and some preliminary results. We also describe some of the additional difficulties that may appear in 2D autofocus: phase residues or branch points and a lack of available redundancy.
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Douglas W. Warner, Dennis C. Ghiglia, Alan Fitzgerrell, and John Beaver "Two-dimensional phase gradient autofocus", Proc. SPIE 4123, Image Reconstruction from Incomplete Data, (16 November 2000);

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