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In image and video coding applications, distortion has been traditionallymeasured using mean square error (MSE), which suggests the use of orthogonaltransforms, such as the discrete cosine transform (DCT). Perceptual metricssuch as Structural Similarity (SSIM) are typically used after encoding, but nottied to the encoding process. In this paper, we consider an alternativeframework where the goal is to optimize a weighted MSE metric, where differentweights can be assigned to each pixel so as to reflect their relativeimportance in terms of perceptual image quality. For this purpose, we propose anovel transform coding scheme based on irregularity-aware graph Fouriertransform (IAGFT), where the induced IAGFT is orthogonal, but the orthogonalityis 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, suchthat the weighted MSE aligns with SSIM. In this way, the associated IAGFT canachieve a coding efficiency improvement in SSIM with respect to conventionaltransform coding based on DCT. Our experimental results show a compression gainin terms of multi-scale SSIM on test images.

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