Synthetic aperture radar (SAR) image registration is an important process in many applications, such as image stitching and remote sensing surveillance. The registration accuracy is commonly affected by the presence of speckle noise in SAR images. When speckle noise is intense, the number of image features acquired by single-feature-based methods is insufficient. An SAR image registration method that combines nonlinear diffusion filtering, Hessian features and edge points is proposed in this paper to reduce speckle noise and obtain more image features. The proposed method uses the infinite symmetric exponential filter (ISEF) for image pre-processing and nonlinear diffusion filtering for scale-space construction. These measures can remove speckle noise from SAR images while preserving image edges. Hessian features and edge points are also employed as image features to optimize the utilization of feature information. Experiments with different noise levels, geometric transformations and image scenes demonstrate that the proposed method effectively improves the accuracy of SAR image registration compared with the SIFT-OCT, SAR-SIFT, Harris-SIFT, NF-Hessian and KAZE-SAR algorithms.