The method of Principal Informative Components (PIC) is presented for problems of statistical measurements, where the signal to be measured cannot be directly observed. Such situations include image reconstruction, system identification, communication channel reversal, media tomography, etc. The common feature of such problems, usually, is instability of their solutions to small variations of initial data that generally require the attraction of special methods of regularization. The basic principle of PIC method consists in employing decomposition of signals in special bases that were formed from eigenvectors of Fischer’s information operator. These bases are related to the method of Principal Components Analysis (PCA), which is well known in statistics, however, they have a somewhat different meaning as compared to the PCA method. The review indicates that by using the special procedures for selecting coordinate vectors, it is possible, first, to guarantee the signal estimation stability to unpredictable factors of problem and, second, to ensure a significant reduction of total measurement error as compared to the “direct” signal estimation, i.e., without the use of basis notions. The review presents a substantiation of PIC method application for problems of linear and nonlinear estimation. The composite technique of coordinate basis optimization is also considered that combines advantages of the physical approach (obviousness and effectiveness) with advantages of statistically informative approach (minimization of statistical errors). The specified technique is based on projecting the arbitrary coordinate basis on PIC subspace. As a result, the range of possible fluctuations of signal estimation is reduced and the upper bound of statistical error of signal measurement is lowered. Some numerical estimates of the PIC method efficiency are given using the example of problem of medium acoustic tomography that confirms the general theoretical conclusions. The review includes the analysis of some information technologies, where the ideas of PIC method hold a good promise for practical application. In particular, it is suggested that one of such promising fields can be MIMO systems that play an important part in 5G wireless access systems.

中文翻译：

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信号参数统计测量问题中的主要信息成分方法（系统评价）

主要信息成分（PIC）方法是针对无法直接观察到待测信号的统计测量问题而提出的。这种情况包括图像重建、系统识别、通信信道反转、媒体断层扫描等。这些问题的共同特征通常是它们对初始数据的小变化的解决方案的不稳定性，这通常需要特殊的正则化方法的吸引力。PIC 方法的基本原理在于在由 Fischer 信息算子的特征向量形成的特殊基中使用信号的分解。这些基数与统计学中众所周知的主成分分析（PCA）方法有关，但是与PCA方法相比，它们的含义有些不同。审查表明，通过使用选择坐标向量的特殊程序，首先可以保证信号估计对不可预测的问题因素的稳定性，其次，与“直接”相比，可以确保显着减少总测量误差。 ”信号估计，即不使用基础概念。该评论提供了 PIC 方法在线性和非线性估计问题中的应用实例。还考虑了坐标基优化的复合技术，它结合了物理方法的优点（显而易见性和有效性）和统计信息方法的优点（最小化统计误差）。指定的技术基于在 PIC 子空间上投影任意坐标基础。因此，减小了信号估计可能出现的波动范围，降低了信号测量统计误差的上限。使用证实一般理论结论的介质声层析成像问题的例子给出了 PIC 方法效率的一些数值估计。审查包括对一些信息技术的分析，其中 PIC 方法的思想在实际应用中具有良好的前景。特别是，有人建议这种有前途的领域之一可以是在 5G 无线接入系统中发挥重要作用的 MIMO 系统。使用证实一般理论结论的介质声层析成像问题的例子给出了 PIC 方法效率的一些数值估计。审查包括对一些信息技术的分析，其中 PIC 方法的思想在实际应用中具有良好的前景。特别是，有人建议这种有前途的领域之一可以是在 5G 无线接入系统中发挥重要作用的 MIMO 系统。使用证实一般理论结论的介质声层析成像问题的例子给出了 PIC 方法效率的一些数值估计。审查包括对一些信息技术的分析，其中 PIC 方法的思想在实际应用中具有良好的前景。特别是，有人建议这种有前途的领域之一可以是在 5G 无线接入系统中发挥重要作用的 MIMO 系统。