Title: Cross-Domain Lossy Compression via Rate- and Classification-Constrained Optimal Transport
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Lossy Compression, Image Compression, Image Restoration, Image Inpainting, Optimal Transport, Multi-task Learning, Rate-Distortion-Perception Tradeoff, Rate-Distortion-Classification Tradeoff, Deep Learning, Unsupervised Learning

Abstract: We study cross-domain lossy compression, where the encoder observes a degraded source while the decoder reconstructs samples from a distinct target distribution. The problem is formulated as constrained optimal transport with two constraints on compression rate and classification loss. With shared common randomness, the one-shot setting reduces to a deterministic transport plan, and we derive closed-form distortion-rate-classification (DRC) and rate-distortion-classification (RDC) tradeoffs for Bernoulli sources under Hamming distortion. In the asymptotic regime, we establish analytic DRC/RDC expressions for Gaussian models under mean-squared error. The framework is further extended to incorporate perception divergences (Kullback-Leibler and squared Wasserstein), yielding closed-form distortion-rate-perception-classification (DRPC) functions. To validate the theory, we develop deep end-to-end compression models for super-resolution (MNIST), denoising (SVHN, CIFAR-10, ImageNet, KODAK), and inpainting (SVHN) problems, demonstrating the consistency between the theoretical results and empirical performance.

TL;DR: We study cross-domain lossy compression via constrained optimal transport with rate and classification constraints, derive closed-form tradeoffs, extend to perception divergences, and validate with deep restoration and inpainting experiments.