Rate-distortion (R-D) function, a key quantity in information theory, characterizes the fundamental limit of how much a data source can be compressed subject to a fidelity criterion, by any compression algorithm. As researchers push for ever-improving compression performance, establishing the R-D function of a given data source is not only of scientific interest, but also sheds light on the possible room for improving compression algorithms. Previous work on this problem relied on distributional assumptions on the data source (Gibson, 2017) or only applied to discrete data. By contrast, this paper makes the first attempt at an algorithm for sandwiching the R-D function of a general (not necessarily discrete) source requiring only i.i.d. data samples. We estimate R-D sandwich bounds on Gaussian and high-dimension banana-shaped sources, as well as GAN-generated images. Our R-D upper bound on natural images indicates room for improving the performance of state-of-the-art image compression methods by 1 dB in PSNR at various bitrates.

翻译：率扭曲功能( R- D) 是信息理论中的一个关键数量, 其特征是数据源在任何压缩算法中按照忠诚标准可以压缩多少数据源的基本限度。 当研究人员推动不断改进压缩性能时, 确定特定数据源的 R- D 函数不仅具有科学意义, 而且还揭示了改进压缩算法的可能空间。 之前关于这一问题的工作依赖于数据源的分布假设( Gibson, 2017年), 或仅适用于离散数据 。 相反, 本文首次尝试用算法来对普通( 不一定离散的) 源的 R- D 函数进行配对, 只需要 i. d. 数据样本。 我们估计高斯 和高离层香蕉形源以及 GAN 生成的图像的 R- D 三明治边框。 我们的自然图像的R- D 绑在自然图像上显示各个位域的 PSNR 中 1 dB 改进最新图像压缩法的性能的空间 。