On a Relation Between the Rate-Distortion Function and Optimal Transport
This provides a theoretical unification for solving scalar quantization and rate-distortion functions using optimal transport methods, which is incremental as it builds on existing connections.
The paper tackles the problem of connecting rate-distortion theory and optimal transport, showing that an entropic optimal transport distance function is equivalent to the rate-distortion function, and numerically verifies this along with links to scalar quantization.
We discuss a relationship between rate-distortion and optimal transport (OT) theory, even though they seem to be unrelated at first glance. In particular, we show that a function defined via an extremal entropic OT distance is equivalent to the rate-distortion function. We numerically verify this result as well as previous results that connect the Monge and Kantorovich problems to optimal scalar quantization. Thus, we unify solving scalar quantization and rate-distortion functions in an alternative fashion by using their respective optimal transport solvers.