Generalized Sampling on Graphs With Subspace and Smoothness Priors
Generalized Sampling on Graphs With Subspace and Smoothness Priors
复制标题
DOI：
10.1109/tsp.2020.2982325
复制
发表时间：
2019-05
影响因子：
5.4
通讯作者：
Yuichi Tanaka;Yonina C. Eldar
中科院分区：
文献类型：
--
作者：
Yuichi Tanaka;Yonina C. Eldar
我们提出了一个框架，广义采样的图形信号，平行采样的移位不变（SI）子空间。该框架允许任意输入信号不受带宽限制。此外，采样和重构滤波器可以不同。我们提出的校正滤波器的设计方法，补偿这些差异，并导致在图形频域中的封闭形式的表达式。在这项研究中，我们考虑两个先验的图形信号：第一个是子空间先验，其中的信号被假定为位于周期图谱（PGS）子空间。PGS子空间是标准采样理论中SI子空间的一种对应形式。第二种是平滑先验，其对图形信号施加平滑要求。我们建议使用恢复技术时，恢复过滤器可以被优化，并在一个设置，其中预定义的过滤器必须使用。采样在图形频域中执行，这是在SI子空间中使用的“通过调制采样”的对应物。我们比较我们的方法与现有的采样技术的图形信号处理。通过几个实验验证了所提出的广义采样方法的有效性。
We propose a framework for generalized sampling of graph signals that parallels sampling in shift invariant (SI) subspaces. This framework allows for arbitrary input signals which are not constrained to be bandlimited. Furthermore, the sampling and reconstruction filters may be different. We present design methods of the correction filter that compensate for these differences and lead to closed form expressions in the graph frequency domain. In this study, we consider two priors on graph signals: The first is a subspace prior, where the signal is assumed to lie in a periodic graph spectrum (PGS) subspace. The PGS subspace is proposed as a counterpart of the SI subspace used in standard sampling theory. The second is a smoothness prior that imposes a smoothness requirement on the graph signal. We suggest the use of recovery techniques when the recovery filter can be optimized and under a setting in which a predefined filter must be used. Sampling is performed in the graph frequency domain, which is a counterpart of “sampling by modulation” used in SI subspaces. We compare our approach with existing sampling techniques on graph signal processing. The effectiveness of the proposed generalized sampling approach is validated numerically through several experiments.