Joint Estimation of Low-Rank Components and Connectivity Graph in High-Dimensional Graph Signals: Application to Brain Imaging

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This paper presents a graph signal processing algorithm to uncover the intrinsic low-rank components and the underlying graph of a high-dimensional, graph-smooth and grossly-corrupted dataset.

• In our problem formulation, we assume that the perturbation on the low-rank components is sparse and the signal is smooth on the graph.
• We propose an algorithm to estimate the low-rank components with the help of the graph and refine the graph with better estimated low-rank components.
• We propose to perform the low-rank estimation and graph refinement jointly so that low-rank estimation can benefit from the refined graph, and graph refinement can leverage the improved low-rank estimation.