论文标题
严格的状态进化分析，用于近似消息传递带有附带信息
Rigorous State Evolution Analysis for Approximate Message Passing with Side Information
论文作者
论文摘要
许多研究领域的一个共同目标是通过嘈杂的线性测量重建未知信号X。近似消息传递（AMP）是一类低复杂性算法，可用于有效地解决此类高维回归任务。通常，在重建过程中可以使用侧面信息（SI）。因此，最近引入了一种将SI纳入AMP中的新型算法框架，该框架将SI纳入AMP，被称为近似信息（amp-si）（AMP-SI）。在这项工作中，当信号和Si对之间存在统计依赖性时，我们为AMP-SI提供了严格的性能保证，并且测量矩阵的条目是独立的，并且分布在高斯。显示AMP-SI性能被证明是通过称为状态进化的标量迭代来追踪的。此外，我们提供的数值示例可以从经验上证明SE可以准确预测AMP-SI均方根误差。
A common goal in many research areas is to reconstruct an unknown signal x from noisy linear measurements. Approximate message passing (AMP) is a class of low-complexity algorithms that can be used for efficiently solving such high-dimensional regression tasks. Often, it is the case that side information (SI) is available during reconstruction. For this reason, a novel algorithmic framework that incorporates SI into AMP, referred to as approximate message passing with side information (AMP-SI), has been recently introduced. In this work, we provide rigorous performance guarantees for AMP-SI when there are statistical dependencies between the signal and SI pairs and the entries of the measurement matrix are independent and identically distributed Gaussian. The AMP-SI performance is shown to be provably tracked by a scalar iteration referred to as state evolution. Moreover, we provide numerical examples that demonstrate empirically that the SE can predict the AMP-SI mean square error accurately.
