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 adressed using algebraic methods by the first author.

翻译：我们研究在图谱域中稀疏的信号，并开发显式算法以从图上的少量顶点样本中重建支持集及部分分量。所需样本数量与图的总规模无关，且仅需考虑图的局部性质。我们的结果基于算子框架的子空间方法，并在谱本征函数在顶点小集上无零点或线性无关时有效。后者最近由第一作者利用代数方法进行了研究。