Cross-Domain Lossy Compression via Rate- and Classification-Constrained Optimal Transport
Nam Nguyen, Thinh Nguyen, Bella Bose
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.
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.
Cross-domain lossy compression unifies rate and classification constraints via optimal transport framework.
- Formulates cross-domain compression as constrained optimal transport with rate and classification constraints
- Derives closed-form DRC and RDC tradeoffs for Bernoulli sources under Hamming distortion
- Extends framework to perception divergences yielding closed-form DRPC functions
- Develops deep end-to-end compression models for super-resolution, denoising, and inpainting
- Optimal transport
- Rate-distortion theory
- Adversarial distribution alignment
- Deep compression networks
- MNIST
- SVHN
- CIFAR-10
- ImageNet
- KODAK
Authors did not state explicit limitations.
Authors did not state explicit future directions.
Author 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
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