# Perceptually inspired weighted MSE optimization using irregularity-aware graph Fourier transform

arXiv: https://arxiv.org/abs/2002.08558 · HTML: https://mlsanity.com/paper/2002.08558/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2020.

## Built on by (most cited first, 2 of 2)

- [Joint Graph and Vertex Importance Learning](https://mlsanity.com/paper/2303.08552/) (2023)
- [Towards Robust Assessment of Pathological Voices via Combined Low-Level Descriptors and Foundation Model Representations](https://mlsanity.com/paper/2505.21356/) (2025)

## Abstract (arXiv)

In image and video coding applications, distortion has been traditionally measured using mean square error (MSE), which suggests the use of orthogonal transforms, such as the discrete cosine transform (DCT). Perceptual metrics such as Structural Similarity (SSIM) are typically used after encoding, but not tied to the encoding process. In this paper, we consider an alternative framework where the goal is to optimize a weighted MSE metric, where different weights can be assigned to each pixel so as to reflect their relative importance in terms of perceptual image quality. For this purpose, we propose a novel transform coding scheme based on irregularity-aware graph Fourier transform (IAGFT), where the induced IAGFT is orthogonal, but the orthogonality is defined with respect to an inner product corresponding to the weighted MSE. We propose to use weights derived from local variances of the input image, such that the weighted MSE aligns with SSIM. In this way, the associated IAGFT can achieve a coding efficiency improvement in SSIM with respect to conventional transform coding based on DCT. Our experimental results show a compression gain in terms of multi-scale SSIM on test images.