Sampling Theory for Graph Signals on Product Graphs
This work addresses the need for more efficient methods in graph signal processing, particularly for multi-modal data, but it is incremental as it extends existing sampling theory to product graphs.
The paper tackles the problem of efficiently sampling and recovering bandlimited graph signals on product graphs, achieving significant savings in sample and computational complexity.
In this paper, we extend the sampling theory on graphs by constructing a framework that exploits the structure in product graphs for efficient sampling and recovery of bandlimited graph signals that lie on them. Product graphs are graphs that are composed from smaller graph atoms; we motivate how this model is a flexible and useful way to model richer classes of data that can be multi-modal in nature. Previous works have established a sampling theory on graphs for bandlimited signals. Importantly, the framework achieves significant savings in both sample complexity and computational complexity