PSNRllä

PSNRllä is a term used to describe a class of PSNR-based quality metrics that extend the classic peak signal-to-noise ratio by incorporating weighting schemes that reflect perceptual importance across an image or video frame. It is not a single fixed formula, but a family of approaches that adapt the standard PSNR calculation with a spatial or perceptual weight map.

In the PSNRllä framework, the standard mean squared error (MSE) is replaced by a weighted MSE. The weighted MSE is computed as the sum over all pixels of w(x,y) times the squared difference between the reference and test images, divided by the sum of the weights: MSE_w = (sum_x,y w(x,y) [I(x,y) − K(x,y)]^2) / (sum_x,y w(x,y)). The PSNRalla value is then PSNRlla = 10 log10 (MAX^2 / MSE_w), where MAX is the maximum possible pixel value. If the weight map w is uniform, PSNRllä reduces to the standard PSNR.

Common variants of PSNRllä use different weight maps, such as saliency-based maps that emphasize visually important regions, contrast-sensitive weights, or locally adaptive weights that reflect texture or edge information. These variants are designed to improve correlation with perceived quality in particular content types or applications, but they remain dependent on the chosen weight map and are not standardized.

Limitations include reliance on an arbitrary or content-specific weight map, potential bias toward certain regions, and mixed correlation with human judgments. PSNRllä can complement traditional metrics (PSNR, SSIM, VMAF) in experimental evaluations, especially when a perceptually informed weighting scheme is appropriate. See also PSNR, SSIM, perceptual quality metrics.