A sparsity-driven approach for SAR image formation and space-variant focusing

In synthetic aperture radar (SAR) imaging, the uncertainties on the position of the sensing platform and on the motion of objects in the observed scene, are important problem sources. These types of uncertainties cause phase errors in the SAR data and subsequently defocusing in the formed image. The defocusing caused by the inexact knowledge of the position of the sensing platform is space-invariant, i.e., the amount of defocusing is same for all points in the scene. However, moving targets in the scene cause space-variant defocusing, i.e., the defocusing arises only in the parts of the image including the moving targets, whereas the stationary background is not defocused. To obtain a focused image, phase errors caused by the moving objects need to be removed. In scenarios involving of multiple point targets moving with different velocities in the scene, considering that the scene to be imaged is usually sparse, we present a sparsity-driven method for joint SAR imaging and removing the defocus caused by moving targets. The proposed method is based on the optimization of a cost function of both the image and phase errors, in a nonquadratic regularization based framework.