On Perceptual Lossy Compression: The Cost of Perceptual Reconstruction and An Optimal Training Framework
This work addresses a fundamental trade-off in compression for applications like media storage and transmission, offering theoretical insights and a practical method, though it is incremental in building on existing perceptual compression research.
The paper tackles the trade-off between distortion and perceptual quality in lossy compression, theoretically showing that perfect perception doubles the lowest achievable MSE distortion and proposing a GAN-based training framework that achieves lower MSE under this constraint.
Lossy compression algorithms are typically designed to achieve the lowest possible distortion at a given bit rate. However, recent studies show that pursuing high perceptual quality would lead to increase of the lowest achievable distortion (e.g., MSE). This paper provides nontrivial results theoretically revealing that, \textit{1}) the cost of achieving perfect perception quality is exactly a doubling of the lowest achievable MSE distortion, \textit{2}) an optimal encoder for the "classic" rate-distortion problem is also optimal for the perceptual compression problem, \textit{3}) distortion loss is unnecessary for training a perceptual decoder. Further, we propose a novel training framework to achieve the lowest MSE distortion under perfect perception constraint at a given bit rate. This framework uses a GAN with discriminator conditioned on an MSE-optimized encoder, which is superior over the traditional framework using distortion plus adversarial loss. Experiments are provided to verify the theoretical finding and demonstrate the superiority of the proposed training framework.