论文标题
支持不确定性原理和图形Rihaczek分布：重新审视和改进
The Support Uncertainty Principle and the Graph Rihaczek Distribution: Revisited and Improved
论文作者
论文摘要
经典的支持不确定性原则指出，信号及其离散的傅立叶变换（DFT）不能同时在时间和频域的任意小区域中定位。时间域和频域中非零样品数量的乘积大或等于信号样本的总数。支持不确定性原理已扩展到信号基础和图形信号的任意正交对，并指出顶点域中的支撑物和光谱域的支持乘积大于基于基础函数的倒数平方最大绝对值。然后将此形式用于压缩感测和稀疏信号处理，以定义重建条件。在本文中，我们将使用图形Rihaczek分布作为分析工具来重新访问图形信号不确定性原理，并为图形信号的支持不确定性原理提供改进的结合。
The classical support uncertainty principle states that the signal and its discrete Fourier transform (DFT) cannot be localized simultaneously in an arbitrary small area in the time and the frequency domain. The product of the number of nonzero samples in the time domain and the frequency domain is greater or equal to the total number of signal samples. The support uncertainty principle has been extended to the arbitrary orthogonal pairs of signal basis and the graph signals, stating that the product of supports in the vertex domain and the spectral domain is greater than the reciprocal squared maximum absolute value of the basis functions. This form is then used in compressive sensing and sparse signal processing to define the reconstruction conditions. In this paper, we will revisit the graph signal uncertainty principle using the graph Rihaczek distribution as an analysis tool and derive an improved bound for the support uncertainty principle of graph signals.
