Reviews: Deep Generative Models for Distribution-Preserving Lossy Compression

The paper proposes a novel problem formulation for lossy compression, namely distribution-preserving lossy compression (DPLC). For a rate constrained lossy compression scheme, for large enough rate of the compression scheme, it is possible to (almost) exactly reconstruct the original signal from its compressed version. However, as the rate gets smaller, the reconstructed signal necessarily has very high distortion. The DPLC formulation aims to alleviate this issue by enforcing an additional constraint during the design of the encoder and the decoder of the compression scheme. The constraint requires that irrespective of the rate of the compression the distribution of the reconstructed signal is the same as that of the original signal.