Is there a relationship between peak-signal-to-noise ratio and structural similarity index measure?

In this study, the authors analyse two well-known image quality metrics, peak-signal-to-noise ratio (PSNR) as well as structural similarity index measure (SSIM), and the authors derive an analytical relationship between them which works for some kinds of common image degradations such as Gaussian blur, additive Gaussian noise, Jpeg and Jpeg2000 compressions. The analytical relationship brings more clarity on the interpretation of PSNR and SSIM values, explains some differences found between these quality measures in the literature and confirms some experimental observations regarding these measures. A series of tests realised on images from the Kodak database give a better understanding of the performance of SSIM and PSNR in assessing image quality.