Estimating SSIM from MSE for DCT-Based Compressed Images

2026-08-03

AI Summary

This work addresses the challenge of accurately estimating the perceptual quality of DCT-compressed images, such as JPEG, using only global mean squared error (MSE) and original image statistics. Existing approaches struggle to effectively approximate the Structural Similarity Index (SSIM) under these constraints. The paper proposes a novel method that redistributes global MSE into local MSE estimates by leveraging the reference image’s local variance or standard deviation, thereby enabling accurate SSIM approximation without requiring ground-truth local error maps. Grounded in the characteristics of DCT-domain compression, the approach naturally extends to video applications. Experimental results on the Kodak and Xiph Subset1 datasets demonstrate that the proposed method significantly outperforms the global MSE baseline across a wide range of JPEG quality levels, achieving both high accuracy and robustness in SSIM estimation.

Abstract

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.

Problem

• SSIM
• MSE
• DCT-based compression
• image quality assessment
• PSNR

Innovation

• SSIM estimation
• MSE redistribution
• DCT-based compression
• reference-derived statistics
• perceptual quality assessment