An algorithm is presented for synthetic aperture radar imaging. This algorithm uses compressed sensing (CS) to reconstruct the image from the signal with low sampling rates in fast and slow times. First, a conventional algorithm is used to obtain the complex image of the target scene. Then, a greedy algorithm is applied to this complex image. It involves the peak search, the estimation of the scattering coefficient, and the removal of the complex image of the target point in each iteration. This algorithm, based on two-dimensional CS, fully utilizes the sparsity of the target scene. By applying the greedy algorithm to the complex image rather than the original signal and by limiting the peak search to a small set of pixels, this algorithm also greatly improves the computational efficiency. In addition, this algorithm is based on blind CS, that is the point spread function is estimated from the signal. This means that this algorithm applies even if the radar parameters are unknown.