Density Aware Blue-Noise Sampling on Graphs

Efficient sampling of graph signals is essential to graph signal processing. Recently, blue-noise was introduced as a sampling method that maximizes the separation between sampling nodes leading to high-frequency dominance patterns, and thus, to high-quality patterns. Despite the simple interpretation of the method, blue-noise sampling is restricted to approximately regular graphs. This study presents an extension of blue-noise sampling that allows the application of the method to irregular graphs. Before sampling with a blue-noise algorithm, the approach regularizes the weights of the edges such that the graph represents a regular structure. Then, the resulting pattern adapts the node's distribution to the local density of the nodes. This work also uses an approach that minimizes the strength of the high-frequency components to recover approximately bandlimited signals. The experimental results show that the proposed methods have superior performance compared to the state-of-the-art techniques.