摘要翻译：
近似消息传递(AMP)是一种有效的线性系统模型迭代稀疏恢复算法。它的性能特点是状态演化(SE)，这是一个简单的标量递归。然而，依赖于测量矩阵集合，AMP可能面临收敛问题。为了避免这一问题，Ma和Ping提出了正交AMP(OAMP)，它采用去相关线性估计和无散度非线性估计。它们也为OAMP提供了SE分析。在SE分析中，我们做了以下两个假设：(i)去相关线性估计量的估计向量由i.i.D。与待估计向量无关的零均值高斯项和(ii)无散度非线性估计器的估计向量由I.I.D。独立于测量矩阵和噪声向量的项。本文利用生成泛函分析(GFA)导出了一个简单的标量递归来刻画迭代稀疏恢复算法，该算法具有无散度估计量，无需消息独立性的假设，从而使我们能够在大系统极限下以精确的方式研究动力学问题。
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英文标题：
《Generating Functional Analysis of Iterative Sparse Signal Recovery
  Algorithms with Divergence-Free Estimators》
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作者：
Kazushi Mimura
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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一级分类：Computer Science        计算机科学
二级分类：Information Theory        信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Mathematics        数学
二级分类：Information Theory        信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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英文摘要：
  Approximate message passing (AMP) is an effective iterative sparse recovery algorithm for linear system models. Its performance is characterized by the state evolution (SE) which is a simple scalar recursion. However, depending on a measurement matrix ensemble, AMP may face a convergence problem. To avoid this problem, orthogonal AMP (OAMP), which uses de-correlation linear estimation and divergence-free non-linear estimation, was proposed by Ma and Ping. They also provide the SE analysis for OAMP. In their SE analysis, the following two assumptions were made: (i) The estimated vector of the de-correlation linear estimator consists of i.i.d. zero-mean Gaussian entries independent of the vector to be estimated and (ii) the estimated vector of the divergence-free non-linear estimator consists of i.i.d. entries independent of the measurement matrix and the noise vector. In this paper, we derive a simple scalar recursion to characterize iterative sparse recovery algorithms with divergence-free estimators without such assumptions of independence of messages by using the generating functional analysis (GFA), which allows us to study the dynamics by an exact way in the large system limit.
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PDF链接：
https://arxiv.org/pdf/1803.11466