Wasserstein distortion is a one-parameter family of distortion measures that was recently proposed to unify fidelity and realism constraints. After establishing continuity results for Wasserstein in the extreme cases of pure fidelity and pure realism, we prove the first coding theorems for compression under Wasserstein distortion focusing on the regime in which both the rate and the distortion are small.

翻译：Wasserstein失真是一类单参数失真测度族，近期被提出用于统一保真度与真实性约束。在确立纯保真度与纯真实性极端情形下Wasserstein失真的连续性结果后，我们针对速率与失真均较小的场景，证明了首个Wasserstein失真约束下的压缩编码定理。