  Contemporary lossy image and video coding standards rely on transform coding,
the process through which pixels are mapped to an alternative representation to
facilitate efficient data compression. Despite impressive performance of
end-to-end optimized compression with deep neural networks, the high
computational and space demands of these models has prevented them from
superseding the relatively simple transform coding found in conventional video
codecs. In this study, we propose learned transforms and entropy coding that
may either serve as (non)linear drop-in replacements, or enhancements for
linear transforms in existing codecs. These transforms can be multi-rate,
allowing a single model to operate along the entire rate-distortion curve. To
demonstrate the utility of our framework, we augmented the DCT with learned
quantization matrices and adaptive entropy coding to compress intra-frame AV1
block prediction residuals. We report substantial BD-rate and perceptual
quality improvements over more complex nonlinear transforms at a fraction of
the computational cost.
