Cross-Domain Lossy Compression via Constrained Minimum Entropy Coupling
For practitioners in image compression and restoration, this work provides a principled information-theoretic framework that integrates rate, distortion, and classification objectives, though the experimental validation is limited to small-scale datasets.
This paper addresses cross-domain lossy compression by formulating a rate-constrained minimum entropy coupling problem with classification constraints. The proposed method achieves improved classification accuracy and more informative reconstructions on MNIST super-resolution and SVHN denoising tasks as the available rate increases.
This paper studies cross-domain lossy compression through the lens of minimum entropy coupling (MEC) with rate and classification constraints. In this setting, an encoder observes samples from a degraded source domain, while the decoder is required to generate outputs following a prescribed target distribution and to preserve information relevant to a downstream classification task. Motivated by logarithmic-loss distortion, we adopt an information-based objective that maximizes the coupling strength between the source and reconstruction, rather than minimizing a sample-wise distortion. Under common randomness, we formulate a rate-constrained MEC problem (MEC-B) and show that the intermediate representation can be removed without loss of optimality, yielding an equivalent deterministic coupling formulation. For Bernoulli sources, closed-form expressions are derived with and without classification constraints. In addition, we implement a neural restoration framework using quantization, entropy modeling, distribution matching, and classification regularization. Experiments on MNIST super-resolution and SVHN denoising show that increasing the available rate improves classification accuracy and yields more informative reconstructions.