Fast compressed sensing SAR imaging using stepped frequency waveform

In recent years, compressed sensing (CS) has been applied to the field of synthetic aperture radar (SAR) imaging and shows great potential. The existing models are, however, based on application of the sensing matrix acquired by exact observation functions. As a result, the corresponding reconstruction algorithms are much more time consuming than traditional matched filter (MF)-based focusing methods, especially in high resolution and wide swath systems. This paper presents a fast compressed sensing SAR imaging method using Omega-K algorithm for stepped frequency waveform. We formulate a new CS-SAR imaging model based on the use of the approximated stepped frequency SAR observation. We incorporate CS and Omega-K algorithm within a sparse regularization framework and then solve it by the iterative thresholding algorithm. The proposed method, named CS-Omega-K, can be applied to high-quality and high-resolution imaging under sub-Nyquist rate sampling, while decreasing the computational cost substantially both in memory and time, resulting in a fast approach. Finally, simulations show that the proposed method can perform stepped frequency SAR imaging effectively below Nyquist sampling rate.