We revisit the Gray-Wyner lossy source coding problem and derive the first-order asymptotic optimal rate-distortion-perception region when additional perception constraints are imposed on reproduced source sequences. The optimal trade-off is shown to be governed by a mutual information term involving common information and two conditional rate-distortion-perception functions. The perception constraint requires that the distribution of each reproduced sequence is close to that of the original source sequence, which is motivated by practical applications in image and video compression. Prior studies usually focus on the compression and reconstruction of a single source sequence. In this paper, we generalize the prior results for point-to-point systems to the representative multi-terminal setting of the Gray-Wyner problem with two correlated source sequences. In particular, we integrate the analyses of the distortion and the perception constraints by including the random circular shift operator in the encoding and decoding process directly.

翻译：本文重新审视Gray-Wyner有损信源编码问题，在重建信源序列上施加额外感知约束的条件下，推导了一阶渐近最优的率-失真-感知区域。研究表明，最优权衡关系由一个涉及公共信息与两个条件率-失真-感知函数的互信息项所决定。感知约束要求每个重建序列的分布接近原始信源序列的分布，该约束的提出受到图像与视频压缩实际应用的驱动。已有研究通常关注单个信源序列的压缩与重建。本文将点对点系统的现有结论推广至具有两个相关信源序列的Gray-Wyner问题这一典型多端设置。特别地，我们通过在编解码过程中直接引入随机循环移位算子，将失真约束与感知约束的分析进行了统一整合。