The nascent field of Rate-Distortion-Perception (RDP) theory is seeing a surge of research interest due to the application of machine learning techniques in the area of lossy compression. The information RDP function characterizes the three-way trade-off between description rate, average distortion, and perceptual quality measured by discrepancy between probability distributions. However, computing RDP functions has been a challenge due to the introduction of the perceptual constraint, and existing research often resorts to data-driven methods. In this paper, we show that the information RDP function can be transformed into a Wasserstein Barycenter problem. The nonstrictly convexity brought by the perceptual constraint can be regularized by an entropy regularization term. We prove that the entropy regularized model converges to the original problem. Furthermore, we propose an alternating iteration method based on the Sinkhorn algorithm to numerically solve the regularized optimization problem. Experimental results demonstrate the efficiency and accuracy of the proposed algorithm.

翻译：率-失真-感知（Rate-Distortion-Perception, RDP）理论这一新兴领域，由于机器学习技术在无损压缩中的应用而受到广泛关注。信息RDP函数刻画了描述速率、平均失真以及由概率分布差异度量的感知质量三者之间的权衡关系。然而，由于感知约束的引入，计算RDP函数一直是一个挑战，现有研究通常借助数据驱动方法。本文证明信息RDP函数可转化为Wasserstein重心问题。感知约束带来的非严格凸性可通过熵正则化项进行修正。我们证明熵正则化模型收敛于原始问题。此外，基于Sinkhorn算法提出一种交替迭代方法，用于数值求解正则化优化问题。实验结果验证了所提算法的效率与准确性。