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.

中文翻译：

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量化随机投影的分布式编码

在本文中，我们提出了一种用于结构化源（例如稀疏信号）的分布式源编码的新框架。我们的框架利用了线性逆问题理论和使用非相干投影的信号表示的最新进展。我们的方法获取并量化信号的非相干线性测量，这些测量表示为单独的位平面。每个位平面都使用适当速率的分布式源代码进行编码并传输。解码器从最不重要的双平面开始，并使用信号的预测作为辅助信息，基于源预测和信号迭代地恢复每个位平面，假设所有先前的低重要性位平面都已经恢复。我们提供指导速率选择的理论结果，仅依赖于源的最小二乘预测误差。这与依赖难以估计的信息理论指标来设置速率的现有方法形成对比。我们使用对遥感多光谱图像的模拟来验证我们的方法，并将它们与具有相似复杂性的现有方法进行比较。