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.

中文翻译：

---

关于感知有损压缩：感知重建的成本和最佳训练框架

有损压缩算法通常设计为在给定比特率下实现尽可能低的失真。然而，最近的研究表明，追求高感知质量会导致最低可实现失真（例如，MSE）的增加。本文提供了重要的结果，从理论上揭示，\textit{1}) 实现完美感知质量的成本恰好是可实现的最低 MSE 失真的两倍，\textit{2}) 是“经典”率失真的最佳编码器问题对于感知压缩问题也是最佳的，\textit{3}) 失真损失对于训练感知解码器是不必要的。此外，我们提出了一种新颖的训练框架，以在给定的比特率下在完美的感知约束下实现最低的 MSE 失真。该框架使用带有以 MSE 优化编码器为条件的鉴别器的 GAN，优于使用失真加对抗性损失的传统框架。提供实验以验证理论发现并证明所提出的训练框架的优越性。