The Support Uncertainty Principle and the Graph Rihaczek Distribution: Revisited and Improved

TL;DR

This paper revisits the support uncertainty principle for graph signals, using the graph Rihaczek distribution to derive an improved bound that enhances understanding of signal localization in graph domains.

Contribution

It introduces an improved bound for the support uncertainty principle of graph signals utilizing the graph Rihaczek distribution as an analysis tool.

Findings

Derived a tighter bound for the support uncertainty principle in graph signals.

Utilized the graph Rihaczek distribution to analyze signal localization.

Enhanced theoretical understanding of graph signal support constraints.

Abstract

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.