Estimating SSIM from MSE for DCT-based compressed images via modeling local error statistics

Efficient and perceptually meaningful quality assessment is a fundamental requirement for image and video processing, compression, and streaming systems. This article shows that, in the context of Discrete Cosine Transform (DCT)-based compressed images, Structural Similarity Index (SSIM) can be approximated from global Peak Signal to Noise Ratio (PSNR) or Mean Square Error (MSE) using local statistics derived only from the reference image. While prior work assumes access to local MSE, we propose two approaches to approximate local MSE by redistributing the global MSE using variance or standard-deviation-based weighting. Experiments on the Kodak and Xiph Subset1 datasets across a range of JPEG quality levels demonstrate that both approaches provide accurate and robust SSIM approximations, substantially outperforming the global MSE baseline. The proposed framework is designed to extend naturally to video, where reference-derived statistics can be amortized across multiple encodes of the same content.