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.
翻译:本手稿通过侧重于压缩感应的特殊问题,探讨了统计力学与估算理论之间的根本联系。我们首先表明,对稀有恢复算法的无症状分析在数学上等同于在热力极限中计算一个旋转玻璃自由能量的问题。然后我们使用统计力学的复制方法来评价无症状系统的性能。无症状结果在通信和信号处理方面有若干应用。我们简要地研究了两个应用实例:分布式压缩感应中所使用的联合稀有恢复算法的特性,以及用于探测空间调制信号的接收器的调整。