论文标题
通过复制方法分析稀疏恢复算法
Analysis of Sparse Recovery Algorithms via the Replica Method
论文作者
论文摘要
该手稿通过关注特定的压缩感应问题，通过统计力学和估计理论之间的基本联系。我们首先表明，稀疏恢复算法的渐近分析在数学上等同于在热力学极限下计算自旋玻璃的自由能的问题。然后，我们使用统计力学中的复制方法来评估渐近状态的性能。渐近结果在通信和信号处理中有多种应用。我们简要介绍了这些应用的两个实例：在分布式压缩传感中使用的关节稀疏恢复算法的表征，以及用于检测空间调制信号的接收器的调整。
This manuscript goes through the fundamental connections between statistical mechanics and estimation theory by focusing on the particular problem of compressive sensing. We first show that the asymptotic analysis of a sparse recovery algorithm is mathematically equivalent to the problem of calculating the free energy of a spin glass in the thermodynamic limit. We then use the replica method from statistical mechanics to evaluate the performance in the asymptotic regime. The asymptotic results have several applications in communications and signal processing. We briefly go through two instances of these applications: Characterization of joint sparse recovery algorithms used in distributed compressive sensing, and tuning of receivers employed for detection of spatially modulated signals.
