  Variable rate is a requirement for flexible and adaptable image and video
compression. However, deep image compression methods are optimized for a single
fixed rate-distortion tradeoff. While this can be addressed by training
multiple models for different tradeoffs, the memory requirements increase
proportionally to the number of models. Scaling the bottleneck representation
of a shared autoencoder can provide variable rate compression with a single
shared autoencoder. However, the R-D performance using this simple mechanism
degrades in low bitrates, and also shrinks the effective range of bit rates.
Addressing these limitations, we formulate the problem of variable
rate-distortion optimization for deep image compression, and propose modulated
autoencoders (MAEs), where the representations of a shared autoencoder are
adapted to the specific rate-distortion tradeoff via a modulation network.
Jointly training this modulated autoencoder and modulation network provides an
effective way to navigate the R-D operational curve. Our experiments show that
the proposed method can achieve almost the same R-D performance of independent
models with significantly fewer parameters.
