Distributed Coding of Quantized Random Projections

TL;DR

This paper introduces a novel distributed source coding framework for structured signals like sparse signals, utilizing incoherent linear measurements and iterative decoding based on source prediction, with theoretical rate guidance and validation on multispectral images.

Contribution

It presents a new distributed coding scheme for structured sources that simplifies rate selection using prediction error, improving upon existing methods.

Findings

Effective coding of incoherent measurements demonstrated

Rate selection guided by prediction error improves performance

Validation on multispectral images shows competitive results

Abstract

In this paper we propose a new framework for distributed source coding of structured sources, such as sparse signals. Our framework capitalizes on recent advances in the theory of linear inverse problems and signal representations using incoherent projections. Our approach acquires and quantizes incoherent linear measurements of the signal, which are represented as separate bitplanes. Each bitplane is coded using a distributed source code of the appropriate rate, and transmitted. The decoder, starts from the least significant biplane and, using a prediction of the signal as side information, iteratively recovers each bitplane based on the source prediction and the signal, assuming all the previous bitplanes of lower significance have already been recovered. We provide theoretical results guiding the rate selection, relying only on the least squares prediction error of the source. This is in contrast to existing approaches which rely on difficult-to-estimate information-theoretic metrics to set the rate. We validate our approach using simulations on remote-sensing multispectral images, comparing them with existing approaches of similar complexity.