Synthetic Aperture Radar (SAR) has the ability to obtain high resolution 2D imagery from distributed targets, such as landscapes. SAR image resolution is limited by the transmitted signal bandwidth and the antenna length, and also depends on the sampling rate. SAR processing is very computer-intensive since it measures and processes enormous amounts of data to obtain the target image. In this paper, we propose an alternative method using compressed sensing (CS), which is able to overcome the fast sampling and the large-scale data storage limitations. CS is also effective for reconstructing the raw image data with sparsity. For complex raw data obtained by the echo signal, compressed sensing based on ℓ1-norm optimization with discrete cosine transform and noiselet processing is adopted to reconstruct the SAR image. By using fewer SAR echo signal samples with complex data, we demonstrate improved results in the SAR image reconstruction.