The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact
The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact
复制标题
高斯矩阵压缩感知的复制对称预测是精确的
DOI：
10.1109/isit.2016.7541382
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
H. Pfister
中科院分区：
文献类型：
--
作者：
G. Reeves;H. Pfister
本文考虑了I.I.D.压缩感测的基本限制。信号分布和I.I.D.高斯测量矩阵。它的主要贡献是在这种情况下对渐近互信息（MI）和最小均方误差（MMSE）的严格表征。在轻度的技术条件下，我们的结果表明，限制MI和MMSE等于统计物理学的复制方法预测的值。这解决了一个众所周知的问题，该问题已经开放了十多年。
This paper considers the fundamental limit of compressed sensing for i.i.d. signal distributions and i.i.d. Gaussian measurement matrices. Its main contribution is a rigorous characterization of the asymptotic mutual information (MI) and minimum mean-square error (MMSE) in this setting. Under mild technical conditions, our results show that the limiting MI and MMSE are equal to the values predicted by the replica method from statistical physics. This resolves a well-known problem that has remained open for over a decade.