In this paper, a novel method for synthetic aperture radar (SAR) imaging is proposed. The approach is based on L 1/2 regularization to reconstruct the scattering field, which optimizes a quadratic error term of the SAR observation process subject to the interested scene sparsity. Compared to the conventional SAR imaging technique, the new method implements SAR imaging effectively at much lower sampling rate than the Nyquist rate, and produces high-quality images with reduced sidelobes and increased resolution. Also, over the prevalent greedy pursuit and L 1 regularization based SAR imaging methods, there are remarkable performance improvements of the new method. On one hand, the new method significantly reduces the number of measurements needed for reconstruction, as supported by a phase transition diagram study. On the other hand, the new method is more robust to the observation noise. These fundamental properties of the new method are supported and demonstrated both by simulations and real SAR data experiments.