Radar imaging is a kind of remote sensing that realizing by Synthetic Aperture Radar (SAR). In SAR, the motion of the radar platform leads to the Synthetic Aperture with long length andSAR imaging is conducted based on the platform motions. Generaly, traditional imaging algorithm like: RDA, CSA and etc. use chirp signal along with match filter. But high rate sampling (due to high operating frequency and needing to both amplitude and phase infotmation for SAR processing), high rate A/D’s, large on board memories and downlink throughput are serious problems of high resolution SAR. In addition, it’s sidelobes lead to an imperfect output. After introducing the Compressive Sensing (CS) theory and the ability of reconstructing sparse signals with lower rate sampling compared with the Nyquist rate, researchers interested in using CS for SAR processing. In these works, they showed that CS can be used in radar imaging and the resulting performance is similar to the traditional algorithms like RDA, CSA, PFA, and etc., but with considerably fewer samples. Many works have been done in the field of CS-SAR so far and different methods are proposed for imaging with CS, reconstructing, sampling, motion compensation and etc. Since most of the SAR signals coefficients are close to zero in the sparse domain, the SAR signal can be defined as a sparse signal. In addition, SAR images usually include sharp bodies such as manmade structures which are strong reflectors. These strong reflections cause a few number of coefficients have higher values than the others. Due to the fact that these coefficients are usually close together and since each strong reflection can affect its near cells, the block sparse model is a better model for the received SAR data. Indeed, if the received SAR data were divided into some blocks with defiend length, then a few number of blocks of them would have considerable values and others would have zero or negligible values. So, the block reconstruction algorithms can be used for reconstructing SAR images.Consequently, in this thesis we propose to use BCS (Block CS) to construct images in SAR. In proposed method, we have conducted sub-sampling with lower rate than the Nyquist rate and then reconstructed with BCS reconstruction algorithms like BOMP. The BCS-SAR can reconstruct SAR images well with considerable fewer samples. In addition, the affect of noise will be discussed in BCS-SAR. Keywords: Synthetic Aperture Radar (SAR), Compressive Sensing (CS), Sub-Nyquest sampling,Block Compressive Sensing (BCS), Block Sparsity
