摘要翻译：
近年来，从信源分离到视频监控等信号处理领域，主成分追踪技术越来越受到人们的重视。到目前为止，所有现有的公式都是实数的，缺乏相位的概念，这是复杂光谱图或彩色图像等输入所固有的。因此，在这封信中，我们将主成分追踪推广到复数和四元数情况，以解释丢失的相位信息。具体地说，我们给出了$\ell_1$-和迹范数正则化子的复和四元数邻近算子。这些算子可以与近似最小化方法结合使用，例如不精确增广拉格朗日乘子算法。然后将新算法应用于声部分离问题，将声部从器乐伴奏中分离出来。在iKala和MSD100数据集上的结果证实了相位信息在主成分追踪中的有用性。
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英文标题：
《Complex and Quaternionic Principal Component Pursuit and Its Application
  to Audio Separation》
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作者：
Tak-Shing T. Chan and Yi-Hsuan Yang
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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：Multimedia        多媒体
分类描述：Roughly includes material in ACM Subject Class H.5.1.
大致包括ACM学科类H.5.1中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Sound        声音
分类描述：Covers all aspects of computing with sound, and sound as an information channel. Includes models of sound, analysis and synthesis, audio user interfaces, sonification of data, computer music, and sound signal processing. Includes ACM Subject Class H.5.5, and intersects with H.1.2, H.5.1, H.5.2, I.2.7, I.5.4, I.6.3, J.5, K.4.2.
涵盖了声音计算的各个方面，以及声音作为一种信息通道。包括声音模型、分析和合成、音频用户界面、数据的可听化、计算机音乐和声音信号处理。包括ACM学科类H.5.5，并与H.1.2、H.5.1、H.5.2、I.2.7、I.5.4、I.6.3、J.5、K.4.2交叉。
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一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Audio and Speech Processing        音频和语音处理
分类描述：Theory and methods for processing signals representing audio, speech, and language, and their applications. This includes analysis, synthesis, enhancement, transformation, classification and interpretation of such signals as well as the design, development, and evaluation of associated signal processing systems. Machine learning and pattern analysis applied to any of the above areas is also welcome.  Specific topics of interest include: auditory modeling and hearing aids; acoustic beamforming and source localization; classification of acoustic scenes; speaker separation; active noise control and echo cancellation; enhancement; de-reverberation; bioacoustics; music signals analysis, synthesis and modification; music information retrieval;  audio for multimedia and joint audio-video processing; spoken and written language modeling, segmentation, tagging, parsing, understanding, and translation; text mining; speech production, perception, and psychoacoustics; speech analysis, synthesis, and perceptual modeling and coding; robust speech recognition; speaker recognition and characterization; deep learning, online learning, and graphical models applied to speech, audio, and language signals; and implementation aspects ranging from system architecture to fast algorithms.
处理代表音频、语音和语言的信号的理论和方法及其应用。这包括分析、合成、增强、转换、分类和解释这些信号，以及相关信号处理系统的设计、开发和评估。机器学习和模式分析应用于上述任何领域也是受欢迎的。感兴趣的具体主题包括：听觉建模和助听器；声波束形成与声源定位；声场景分类；说话人分离；有源噪声控制和回声消除；增强；去混响；生物声学；音乐信号的分析、合成与修饰；音乐信息检索；多媒体音频和联合音视频处理；口语和书面语建模、切分、标注、句法分析、理解和翻译；文本挖掘；言语产生、感知和心理声学；语音分析、合成、感知建模和编码；鲁棒语音识别；说话人识别与特征描述；应用于语音、音频和语言信号的深度学习、在线学习和图形模型；以及从系统架构到快速算法的实现方面。
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一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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英文摘要：
  Recently, the principal component pursuit has received increasing attention in signal processing research ranging from source separation to video surveillance. So far, all existing formulations are real-valued and lack the concept of phase, which is inherent in inputs such as complex spectrograms or color images. Thus, in this letter, we extend principal component pursuit to the complex and quaternionic cases to account for the missing phase information. Specifically, we present both complex and quaternionic proximity operators for the $\ell_1$- and trace-norm regularizers. These operators can be used in conjunction with proximal minimization methods such as the inexact augmented Lagrange multiplier algorithm. The new algorithms are then applied to the singing voice separation problem, which aims to separate the singing voice from the instrumental accompaniment. Results on the iKala and MSD100 datasets confirmed the usefulness of phase information in principal component pursuit.
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PDF链接：
https://arxiv.org/pdf/1801.03816