We study signals that are sparse in graph spectral domain and develop explicit algorithms to reconstruct the support set as well as partial components from samples on few vertices of the graph. The number of required samples is independent of the total size of the graph and takes only local properties of the graph into account. Our results rely on an operator based framework for subspace methods and become effective when the spectral eigenfunctions are zero-free or linear independent on small sets of the vertices. The latter has recently been addressed using algebraic methods by the first author.

中文翻译：

---

频率稀疏图信号的两种子空间方法


我们研究图谱域中稀疏的信号，并开发显式算法来重建支持集以及来自图几个顶点上的样本的部分分量。所需样本的数量与图形的总大小无关，并且仅考虑图形的局部属性。我们的结果依赖于基于算子的子空间方法框架，当谱特征函数在小顶点集上无零或线性无关时变得有效。后者最近由第一作者使用代数方法解决。