Reduced-reference image quality assessment (RR-IQA) provides a practical solution for automatic image quality evaluations in various applications where only partial information about the original reference image is accessible. In this paper, we propose an RR-IQA method by estimating the structural similarity index (SSIM), which is a widely used full-reference (FR) image quality measure shown to be a good indicator of perceptual image quality. Specifically, we extract statistical features from a multiscale multiorientation divisive normalization transform and develop a distortion measure by following the philosophy in the construction of SSIM. We find an interesting linear relationship between the FR SSIM measure and our RR estimate when the image distortion type is fixed. A regression-by-discretization method is then applied to normalize our measure across image distortion types. We use six publicly available subject-rated databases to test the proposed RR-SSIM method, which shows strong correlations with both SSIM and subjective quality evaluations. Finally, we introduce the novel idea of partially repairing an image using RR features and use deblurring as an example to demonstrate its application.