Focusing in synthetic aperture radar by multiresolution methods

In synthetic aperture radar (SAR) and inverse synthetic aperture radar (ISAR), the problem usually referred to as motion through resolution cells defocuses the radar image leading to significant loss of detection probability. This problem is traditionally compensated for at the SAR image formation process by using more computationally intensive methods. As the resolution of the SAR system increases, with longer integration times, it is becoming increasingly more difficult to correct for these defocusing effects. This problem is made worse with moving targets since it is harder to assign the target to a specific cell during the entire synthetic aperture interval. By analyzing the image formation process in SAR/ISAR systems, we observe that the defocused image of a SAR/ISAR target can be modeled as a superposition of space shifted replicas of the focused target signature. In this paper, we present a robust, simple detector that combines in a coherent way the energy in the different replicas to focus the image and provide increased resolution. Our approach approximates the maximum likelihood estimate of the defocused target signature (hard to determine) by the orthogonal projection onto a subspace that is close (in some sense) to the subspace generated by the multiple shifted replicas of the focused target signature. We apply multiresolution techniques to design the approximating subspace.