支持度不确定性原理与图Rihaczek分布的再认识与改进
The Support Uncertainty Principle and the Graph Rihaczek Distribution: Revisited and Improved
摘要：
经典的支撑不确定性原理指出，信号及其离散傅里叶变换（DFT）不能同时在时域和频域中的任意小区域中局部化。时域和频域中的非零样本的数量的乘积大于或等于信号样本的总数。支持度不确定性原理被推广到任意正交的信号基和图信号对，指出顶点域和谱域的支持度的乘积大于基函数的倒数平方最大绝对值。然后，在压缩感测和稀疏信号处理中使用该形式来定义重构条件。在本文中，我们将重新使用图Rihaczek分布作为分析工具的图信号的不确定性原则，并推导出一个改进的边界的支持度不确定性原则的图信号。
英文摘要：
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.
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