New method improves sequential data compression balancing error and perception
Sequential Lossy Compression With Causal Conditional Perception
Information Theory
Summary
This paper looks at how to compress sequences of data (like audio or video) while keeping the compressed version looking or sounding close to the original in a meaningful way. The authors focus on compressing data step-by-step without looking ahead, ensuring the reconstructed data matches the perception of the original when considering the past data. They develop mathematical tools and formulas to find the best compression rate when trying to balance accuracy and how the output is perceived. Their approach applies to certain statistical models of data and includes exact solutions for Gaussian cases, extending known results in data compression.
What this means in practice
- •For video streaming engineers: Design real-time video compression that maintains perceived quality based on past frame data for smoother streaming under bandwidth limits.
- •For audio codec developers: Create audio compression algorithms that adaptively balance error and sound quality perception using sequential models for live transmissions.
Authors
Photios A. Stavrou, Zixuan He
Abstract
In this paper, we study sequential lossy compression under a causal conditional perception criterion comparing source and reconstruction distributions given the same reconstruction history. For first-order Markov sources, we formulate the finite-horizon nonanticipative rate-distortion-perception function (NRDPF) with stagewise constraints and establish one-shot lower and upper bounds on the minimum variable-length sum rate using a strengthened strong functional-representation lemma (SFRL) and common randomness. For time-varying scalar Gauss--Markov sources under pointwise mean-squared error (MSE) and conditional squared Wasserstein-$2$ fidelity, we prove Gaussian optimality, derive a log-variance characterization, and obtain a closed-form solution that recovers the classical Gaussian nonanticipative rate-distortion function (NRDF) when perception is unconstrained and the classical Gaussian RDPF when the source is stationary and memoryless.