Automatic target detection (ATD) methods for synthetic aperture radar (SAR) imagery are sensitive to image resolution, target size, clutter complexity, and speckle noise level. However, a robust ATD method needs to be less sensitive to the above factors. In this study, a constant false alarm rate (CFAR) based method is proposed which can perform target detection independent of image resolution and target size even in heterogeneous background clutter. The proposed method is computationally efficient since clutter statistics are calculated only for candidate target regions and a single execution of the method is sufficient for different types of targets having different shapes and sizes. Computational efficiency is further increased by parallelizing the algorithm using OpenMP and NVidia CUDA implementations.