结构化传感矩阵相位恢复线性化消息传递的普适性
Universality of Linearized Message Passing for Phase Retrieval with Structured Sensing Matrices
摘要：
在相位恢复问题中，试图从形式为$y_i = |(\mathbf{A} \mathbf{x})_i|$的$m$测量中恢复未知的$n$维信号矢量$\mathbf{x}$，其中$\mathbf{A}$表示感测矩阵。许多算法都是基于近似消息传递的。对于这些算法，已知如果感测矩阵$n$是通过对均匀随机（即，Haar分布）正交矩阵，在高维渐近区域（$m,n \rightarrow \infty, n/m \rightarrow κ$）中，算法的动力学由称为状态演化的确定性递归给出。对于一类特殊的线性化的消息传递算法，我们表明，状态演变是普遍的：它继续持有，即使当$\mathbf{A}$是由随机子采样列的Hadamard-Walsh矩阵，提供的信号是从高斯先验。
英文摘要：
In the phase retrieval problem one seeks to recover an unknown $n$ dimensional signal vector $\mathbf{x}$ from $m$ measurements of the form $y_i = |(\mathbf{A} \mathbf{x})_i|$, where $\mathbf{A}$ denotes the sensing matrix. Many algorithms for this problem are based on approximate message passing. For these algorithms, it is known that if the sensing matrix $\mathbf{A}$ is generated by sub-sampling $n$ columns of a uniformly random (i.e., Haar distributed) orthogonal matrix, in the high dimensional asymptotic regime ($m,n \rightarrow \infty, n/m \rightarrow κ$), the dynamics of the algorithm are given by a deterministic recursion known as the state evolution. For a special class of linearized message-passing algorithms, we show that the state evolution is universal: it continues to hold even when $\mathbf{A}$ is generated by randomly sub-sampling columns of the Hadamard-Walsh matrix, provided the signal is drawn from a Gaussian prior.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
