Slepian guided filtering of graph signals

Miljan Petrović; Dimitri Van De Ville

doi:10.1117/12.2528827

9 September 2019 Slepian guided filtering of graph signals

Proceedings Volume 11138, Wavelets and Sparsity XVIII; 111380D (2019) https://doi.org/10.1117/12.2528827
Event: SPIE Optical Engineering + Applications, 2019, San Diego, California, United States

Abstract

Joint localization of graph signals in vertex and spectral domain is achieved in Slepian vectors calculated by either maximizing energy concentration (μ) or minimizing modified embedded distance (ξ) in the subgraph of interest. On the other hand, graph Laplacian is extensively used in graph signal processing as it defines graph Fourier transform (GFT) and operators such as filtering, wavelets, etc. In the context of modeling human brain as a graph, low pass (smooth over neighboring nodes) filtered graph signals represent a valuable source of information known as aligned signals. Here, we propose to define GFT and graph filtering using Slepian orthogonal basis. We explored power spectrum density estimates of random signals on Erdős-Rényi graphs and determined local discrepancies in signal behavior which cannot be accessed by the graph Laplacian, but are detected by the Slepian basis. This motivated the application of Slepian guided graph signal filtering in neuroimaging. We built a graph from diffusion-weighed brain imaging data and used blood-oxygenation-level-dependent (BOLD) time series as graph signals residing on its nodes. The dataset included recordings of 21 subjects performing a working memory task. In certain brain regions known to exhibit activity negatively correlated to performing the task, the only method capable of identifying this type of behavior in the bandlimited framework was ξ-Slepian guided filtering. The localization property of the proposed approach provides significant contribution to the strength of the graph spectral analysis, as it allows inclusion of a priori knowledge of the explored graph's mesoscale structure.

Citation Download Citation

Miljan Petrović and Dimitri Van De Ville "Slepian guided filtering of graph signals", Proc. SPIE 11138, Wavelets and Sparsity XVIII, 111380D (9 September 2019); https://doi.org/10.1117/12.2528827

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