Lossy compression algorithms are typically designed to achieve the lowest possible distortion at a given bit rate. However, recent studies show that pursuing high perceptual quality would lead to increase of the lowest achievable distortion (e.g., MSE). This paper provides nontrivial results theoretically revealing that, \textit{1}) the cost of achieving perfect perception quality is exactly a doubling of the lowest achievable MSE distortion, \textit{2}) an optimal encoder for the "classic" rate-distortion problem is also optimal for the perceptual compression problem, \textit{3}) distortion loss is unnecessary for training a perceptual decoder. Further, we propose a novel training framework to achieve the lowest MSE distortion under perfect perception constraint at a given bit rate. This framework uses a GAN with discriminator conditioned on an MSE-optimized encoder, which is superior over the traditional framework using distortion plus adversarial loss. Experiments are provided to verify the theoretical finding and demonstrate the superiority of the proposed training framework.

翻译：失传压缩算法通常旨在以一定速度达到最低可能的扭曲。然而,最近的研究表明,追求高感官质量会导致可达到的最低扭曲(例如,MSE)的增加。本文从理论上提供了非技术性的结果,从理论上表明,实现完美感知质量的成本是最低可达到的MSE扭曲值的两倍,\textit{2})“经典”率扭曲问题的最佳编码器对于概念压缩问题也是最佳的, \textit{3}) 扭曲损失对于培训一种概念解码器来说是不必要的。 此外,我们提出一个新的培训框架,以达到最低的MSE扭曲值,但有一定比例的完美感约束。这个框架使用一种带有歧视条件的GAN,其条件是MSE-optimizedencoder, 它比使用扭曲和对抗性损失的传统框架优越。提供了实验,以核实理论发现和证明拟议培训框架的优越性。