Sampling Set Selection for Graph Signals under Arbitrary Signal Priors
Sampling Set Selection for Graph Signals under Arbitrary Signal Priors
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DOI：
10.1109/icassp43922.2022.9747703
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发表时间：
2022-05
期刊：
影响因子：
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通讯作者：
Junya Hara;Yuichi Tanaka
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文献类型：
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作者：
Junya Hara;Yuichi Tanaka
提出了一种任意先验条件下图信号采样集的选择方法。大多数图信号采样方法都假定信号是带宽受限的。然而，在实际情况中，存在许多像分段平滑/恒定信号这样的全频带图形信号。我们的采样集选择方法允许任意图形信号模型，只要它们是线性的。这可以从一个普遍的抽样框架中得出。与已有的工作不同，我们主要研究采样子空间和重构子空间之间的直和条件，其中直和条件对采样信号的最佳恢复起着关键作用。在此基础上，设计了一种基于Neumann级数逼近的快速采样集选择算法。在采样和恢复实验中，我们对几种图信号模型验证了该方法的有效性。
We propose a sampling set selection method for graph signals under arbitrary signal priors. Most approaches of graph signal sampling assume that signals are bandlimited. However, in practical situations, there exist many full-band graph signals like piecewise smooth/constant signals. Our sampling set selection method allows for arbitrary graph signal models as long as they are linear. This can be derived from a generalized sampling framework. In contrast to existing works, we focus on the direct sum condition between sampling and reconstruction subspaces where the direct sum condition plays a key role for the best possible recovery of sampled signals. We also design a fast sampling set selection algorithm based on the proposed method with the Neumann series approximation. In sampling and recovery experiments, we validate the effectiveness of the proposed method for several graph signal models.