摘要翻译：
我们考虑了从高斯随机游走的抽取版本的有损压缩估计高斯随机游走的问题。因此，编码器对抽取的随机游动进行操作，解码器根据其编码版本在均方误差(MSE)准则下估计原始随机游动。众所周知，该问题中的最小失真是通过估计压缩（estimate-and-compress，EC)信源编码策略来实现的，在该策略中，编码器首先估计原始随机游动，然后在比特约束下压缩该估计。在本工作中，我们导出了这个最小失真作为比特率和抽取因子的函数的闭式表达式。其次，我们考虑了压缩-估计(CE)信源编码方案，其中编码器首先根据MSE准则（相对于抽取序列）对抽取序列进行压缩，原始随机游动仅在解码器处估计。我们用一个封闭的形式计算了CE下的失真，并证明了两种方案下的失真之间存在一个非零的间隙。这种性能上的差异说明了在编码器中具有抽取因子的重要性。
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英文标题：
《Lossy Compression of Decimated Gaussian Random Walks》
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作者：
Georgia Murray, Alon Kipnis, and Andrea J. Goldsmith
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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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英文摘要：
  We consider the problem of estimating a Gaussian random walk from a lossy compression of its decimated version. Hence, the encoder operates on the decimated random walk, and the decoder estimates the original random walk from its encoded version under a mean squared error (MSE) criterion. It is well-known that the minimal distortion in this problem is attained by an estimate-and-compress (EC) source coding strategy, in which the encoder first estimates the original random walk and then compresses this estimate subject to the bit constraint. In this work, we derive a closed-form expression for this minimal distortion as a function of the bitrate and the decimation factor. Next, we consider a compress-and-estimate (CE) source coding scheme, in which the encoder first compresses the decimated sequence subject to an MSE criterion (with respect to the decimated sequence), and the original random walk is estimated only at the decoder. We evaluate the distortion under CE in a closed form and show that there exists a nonzero gap between the distortion under the two schemes. This difference in performance illustrates the importance of having the decimation factor at the encoder.
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PDF链接：
https://arxiv.org/pdf/1802.0958