This paper presents the problem of block simplex constrained signal recovery, which has been demonstrated to be a suitable formulation for estimation problems in networks such as route flow estimation in traffic. There are several natural approaches to this problem: compressed sensing, Bayesian inference, and convex optimization. This paper presents new methods within each framework and assesses their respective abilities to reconstruct signals, with the particular emphasis on sparse recovery, ability to incorporate prior information, and scalability. We then apply these methods to route flow estimation in traffic networks of various sizes and network topologies. We find that both compressed sensing and Bayesian inference approaches are appropriate for structured recovery but have scalability limitations. The convex optimization approach does not directly incorporate prior information, but scales well and has been shown to achieve 90% route flow accuracy on a full-scale network of over 10 000 links and 280 000 routes on a synthetic benchmark based on the I-210 corridor near Los Angeles, CA, USA.

中文翻译：

---

块单纯形信号恢复：方法、权衡和路由应用

本文提出了块单纯形约束信号恢复问题，该问题已被证明是一种适用于网络中估计问题的公式，例如交通中的路由流估计。这个问题有几种自然的方法：压缩感知、贝叶斯推理和凸优化。本文介绍了每个框架内的新方法，并评估了它们各自重建信号的能力，特别强调稀疏恢复、合并先验信息的能力和可扩展性。然后，我们将这些方法应用于各种规模和网络拓扑的交通网络中的路由流估计。我们发现压缩感知和贝叶斯推理方法都适用于结构化恢复，但具有可扩展性限制。