Abstract: A novel statistical decision criterion for Synthetic Aperture Radar (SAR) image resolution is presented here. The classic Rayleigh resolution criterion is based on the human visual perception and is defective in theory to some degree. Especially there exist two problems for Rayleigh resolving criterion in the application of SAR image resolution: the influence of noise on resolving ability of imaging system is not demonstrated and the complex image can not be applied by this classic criterion, which is a restriction for the wide application of SAR image. By analyzing the resolving performance of SAR image, the target discrimination is regarded as a hypothesis test problem in this paper. Thus the corresponding hypothesis test model is constructed and a corresponding statistical decision criterion for SAR image resolution is also put forward. As for target discrimination in the power spectrum image and the complex image, two main conclusions are obtained, one is the explicit relation between the resolution and signal-noise-ratio, the other is the explicit relation between the resolution and target relative phase. These conclusions are very significant for the SAR system design, image super resolution and image application.