Joint image formation and two-dimensional autofocusing for synthetic aperture radar data

Imaging via synthetic aperture radar (SAR) is a well-established technique for effective scene reconstruction, with resolution up to a few centimeters. The measurement process requires the round trip time for the electromagnetic waves to travel to the scene and return back to the sensing mechanism. While hypothetically the round trip time can be exactly determined, in practice this distance can only be approximated, leading to errors in the round trip time estimates. These errors manifest as phase errors on the data and produce defocused imagery, making information extraction difficult. This investigation develops an autofocusing technique that exploits the correlation of the phase error on both the azimuth angle and spatial (cycles/meter) frequencies while also enforcing the piecewise smooth nature of the image. Our method estimates the phase error correction and the image through a joint optimization procedure. Specifically, our method incorporates a phase synchronization technique to estimate the unknown two-dimensional phase error. High order regularization is used in the optimization procedure, which helps to reduce speckle in the SAR image.