Signal recovery from unitarily invariant measurements is investigated in this paper. A message-passing algorithm is formulated on the basis of expectation propagation (EP). A rigorous analysis is presented for the dynamics of the algorithm in the large system limit, where both input and output dimensions tend to infinity while the compression rate is kept constant. The main result is the justification of state evolution (SE) equations conjectured by Ma and Ping. This result implies that the EP-based algorithm achieves the Bayes-optimal performance that was originally derived via a non-rigorous tool in statistical physics and proved partially in a recent paper, when the compression rate is larger than a threshold. The proof is based on an extension of a conventional conditioning technique for the standard Gaussian matrix to the case of the Haar matrix.

中文翻译：

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从Unit不变测量中基于期望传播的信号恢复的严格动力学

本文研究了单位不变测量的信号恢复。基于期望传播（EP）制定了消息传递算法。针对大系统限制中算法的动力学特性，进行了严格的分析，其中输入和输出尺寸都趋于无穷大，而压缩率保持恒定。主要结果是由Ma和Ping猜想出的状态演化（SE）方程的合理性。该结果表明，基于EP的算法实现了贝叶斯最佳性能，该性能最初是通过统计物理学中的非严格工具得出的，并且在最近的论文中部分证明了当压缩率大于阈值时。