  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.
