Image formation algorithms in a variety of applications have explicit or implicit dependence on a mathematical model of the observation process. Inaccuracies in the observation model may cause various degradations and artifacts in the reconstructed images. The application of interest in this paper is synthetic aperture radar (SAR) imaging, which particularly suffers from motion-induced model errors. These types of errors result in phase errors in SAR data, which cause defocusing of the reconstructed images. Particularly focusing on imaging of fields that admit a sparse representation, we propose a sparsity-driven method for joint SAR imaging and phase error correction. Phase error correction is performed during the image formation process. The problem is set up as an optimization problem in a nonquadratic regularization-based framework. The method involves an iterative algorithm, where each iteration of which consists of consecutive steps of image formation and model error correction. Experimental results show the effectiveness of the approach for various types of phase errors, as well as the improvements that it provides over existing techniques for model error compensation in SAR.

In synthetic aperture radar (SAR) imaging, the presence of moving targets in the scene causes phase errors in the SAR data and subsequently defocusing in the formed image. The defocusing caused by the moving targets exhibits space-variant characteristics, i.e., the defocusing arises only in the parts of the image containing the moving targets, whereas the stationary background is not defocused. Considering that the reflectivity field to be imaged usually admits sparse representation, we propose a sparsity-driven method for joint SAR imaging and removing the defocus caused by moving targets. The method is performed in a nonquadratic regularization based framework by solving an optimization problem, in which prior information about both the scene and phase errors are incorporated as constraints.

Solution of inverse problems in imaging requires the use of a mathematical model of the observation process. However such models often involve errors and uncertainties themselves. The application of interest in this paper is synthetic aperture radar (SAR) imaging, which particularly suffers from motion-induced model errors. These types of errors result in phase errors in SAR data which cause defocusing of the reconstructed image. Mostly, phase errors vary only in cross-range direction. However, in many situations, it is possible to encounter 2D phase errors, which are both range and cross-range dependent. We propose a sparsity-driven method for joint SAR imaging and correction of 1D as well as 2D phase errors. This method performs phase error correction during the image formation process and provides focused, high-resolution images. Experimental results show the effectiveness of the approach.