When comparing learned image/video restoration and compression methods, it is common to report peak-signal to noise ratio (PSNR) results. However, there does not exist a generally agreed upon practice to compute PSNR for sets of images or video. Some authors report average of individual image/frame PSNR, which is equivalent to computing a single PSNR from the geometric mean of individual image/frame mean-square error (MSE). Others compute a single PSNR from the arithmetic mean of frame MSEs for each video. Furthermore, some compute the MSE/PSNR of Y-channel only, while others compute MSE/PSNR for RGB channels. This paper investigates different approaches to computing PSNR for sets of images, single video, and sets of video and the relation between them. We show the difference between computing the PSNR based on arithmetic vs. geometric mean of MSE depends on the distribution of MSE over the set of images or video, and that this distribution is task-dependent. In particular, these two methods yield larger differences in restoration problems, where the MSE is exponentially distributed and smaller differences in compression problems, where the MSE distribution is narrower. We hope this paper will motivate the community to clearly describe how they compute reported PSNR values to enable consistent comparison.

中文翻译：

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关于一组图像或视频的PSNR的计算

在比较学习的图像/视频恢复和压缩方法时，通常会报告峰值信噪比（PSNR）结果。但是，不存在为图像或视频集计算PSNR的公认方法。一些作者报告了单个图像/帧PSNR的平均值，这等效于根据单个图像/帧均方误差（MSE）的几何平均值计算单个PSNR。其他人则根据每个视频的帧MSE的算术平均值来计算单个PSNR。此外，有些只计算Y通道的MSE / PSNR，而另一些只计算RGB通道的MSE / PSNR。本文研究了用于计算图像集，单个视频和视频集的PSNR的不同方法，以及它们之间的关系。我们展示了基于算术vs. MSE的几何平均值取决于MSE在图像或视频集上的分布，并且这种分布取决于任务。特别是，这两种方法在恢复问题（MSE呈指数分布）中产生较大差异，在压缩问题中（MSE分布较窄）产生较小差异。我们希望本文能够激励社区明确描述他们如何计算报告的PSNR值，以实现一致的比较。