图上的离散线性典型变换:不确定性原理与采样

IF 3.4 2区 工程技术 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC
Yu Zhang , Bing-Zhao Li
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引用次数: 0

摘要

随着越来越多的经典信号处理方法涌入图信号处理领域,以离散线性典型变换为基础的方法在图信号中得到了应用。在本文中,我们首先提出了图线性典型变换(GLCT)的不确定性原理,该原理基于一类在顶点和图谱域都最大程度集中的图信号。随后,利用不确定性原理,我们建立了从样本子集恢复 GLCT 带限信号的条件,从而提出了 GLCT 的采样理论。我们阐明了不确定性原理与采样之间的有趣联系。此外,通过采用采样集选择和实验设计采样策略,我们引入了 GLCT 领域的最优采样算子。最后,我们通过模拟和数值实验评估了我们的方法在各种应用中的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Discrete linear canonical transform on graphs: Uncertainty principle and sampling

With an increasing influx of classical signal processing methodologies into the field of graph signal processing, approaches grounded in discrete linear canonical transform have found application in graph signals. In this paper, we initially propose the uncertainty principle of the graph linear canonical transform (GLCT), which is based on a class of graph signals maximally concentrated in both vertex and graph spectral domains. Subsequently, leveraging the uncertainty principle, we establish conditions for recovering bandlimited signals of the GLCT from a subset of samples, thereby formulating the sampling theory for the GLCT. We elucidate interesting connections between the uncertainty principle and sampling. Further, by employing sampling set selection and experimental design sampling strategies, we introduce optimal sampling operators in the GLCT domain. Finally, we evaluate the performance of our methods through simulations and numerical experiments across applications.

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来源期刊
Signal Processing
Signal Processing 工程技术-工程:电子与电气
CiteScore
9.20
自引率
9.10%
发文量
309
审稿时长
41 days
期刊介绍: Signal Processing incorporates all aspects of the theory and practice of signal processing. It features original research work, tutorial and review articles, and accounts of practical developments. It is intended for a rapid dissemination of knowledge and experience to engineers and scientists working in the research, development or practical application of signal processing. Subject areas covered by the journal include: Signal Theory; Stochastic Processes; Detection and Estimation; Spectral Analysis; Filtering; Signal Processing Systems; Software Developments; Image Processing; Pattern Recognition; Optical Signal Processing; Digital Signal Processing; Multi-dimensional Signal Processing; Communication Signal Processing; Biomedical Signal Processing; Geophysical and Astrophysical Signal Processing; Earth Resources Signal Processing; Acoustic and Vibration Signal Processing; Data Processing; Remote Sensing; Signal Processing Technology; Radar Signal Processing; Sonar Signal Processing; Industrial Applications; New Applications.
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