The aim of this paper is to show how the structural similarity metric SSIM for image quality assessment can be seen in many cases, such as DCT-based compressed images and video, as a content-aware version of the peak signal-to-noise ratio (PSNR). In fact, under some assumptions described in the paper, the first can be derived directly from the latter based on a single content-dependent parameter, i.e. the variance of the image / video frame.