Blue-Noise Sampling on Graphs
Blue-Noise Sampling on Graphs
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DOI：
10.1109/tsipn.2019.2922852
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发表时间：
2018-11
影响因子：
3.2
通讯作者：
Alejandro Parada-Mayorga;D. Lau;Jhony H. Giraldo;G. Arce
中科院分区：
文献类型：
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作者：
Alejandro Parada-Mayorga;D. Lau;Jhony H. Giraldo;G. Arce
在图信号处理领域，图是由加权链路任意连接的节点集合；图信号是与每个节点相关联的标量值的集合；采样是选择最优节点子集的问题，从这些节点子集中可以重构图信号。本文提出在图的顶点域上使用空间抖动，作为一种方便地找到统计上好的采样集的方法。这是建立了在顶点域上存在一组良好的采样集，通过采样节点之间的距离最大化来表征；在傅里叶域中，它们的特征是由高频占主导的频谱，称为蓝噪声。图上的蓝噪声采样与先前图信号处理结果之间的理论联系也被建立，解释了该方法的优点。将我们的分析限制在无向图和连通图上，为了比较蓝噪声采样与其他方法的有效性，进行了数值测试。
In the area of graph signal processing, a graph is a set of nodes arbitrarily connected by weighted links; a graph signal is a set of scalar values associated with each node; and sampling is the problem of selecting an optimal subset of nodes from which a graph signal can be reconstructed. This paper proposes the use of spatial dithering on the vertex domain of the graph, as a way to conveniently find statistically good sampling sets. This is done establishing that there is a family of good sampling sets characterized on the vertex domain by a maximization of the distance between sampling nodes; in the Fourier domain, these are characterized by spectrums that are dominated by high frequencies referred to as blue-noise. The theoretical connection between blue-noise sampling on graphs and previous results in graph signal processing is also established, explaining the advantages of the proposed approach. Restricting our analysis to undirected and connected graphs, numerical tests are performed in order to compare the effectiveness of blue-noise sampling against other approaches.