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Euler’s Elastica Regularization for Voxel Selection of fMRI Data

Chuncheng Zhang1 and Zhiying Long2
1.Institute of Automation, Chinese Academy of Sciences, Beijing, China
2.State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China
Abstract—Multivariate analysis methods have been widely applied to functional Magnetic Resonance Imaging (fMRI) data to reveal brain activity patterns and decode brain states. Among the various multivariate analysis methods, the multivariate regression models that take high-dimensional fMRI data as inputs while using relevant regularization were proposed for voxel selection or decoding. Although some previous studies added the sparse regularization to the multivariate regression model to select relevant voxels, the selected sparse voxels cannot be used to map brain activity of each task. Compared to the sparse regularization, the Euler’s Elastica (EE) regularization that considers the spatial information of data can identify the clustered voxels of fMRI data. Our previous study added EE Regularization to Logical Regression (EELR) and demonstrated its advantages over the other regularizations in fMRI-based decoding. In this study, we further developed a multivariate regression model using EE in 3D space as constraint for voxel selection. We performed experimental tests on both simulated data and real fMRI data to investigate the feasibility and robustness of EE regression model. The performance of EE regression was compared with the Generalized Linear Model (GLM) and Total Variation (TV) regression in brain activity detection, and was compared with GLM, Laplacian Smoothed L0 norm (LSL0) and TV regression methods in feature selection for brain state decoding. The results indicated that EE regression possessed better sensitivity to detect brain regions specific to a task than did GLM and better spatial detection power than TV regression. Moreover, EE regression outperformed GLM, LSL0 and TV in feature selection. 

Index Terms—fMRI, decoding, feature selection, Euler’s elastica, multivariate regression

Cite: Chuncheng Zhang and Zhiying Long, "Euler’s Elastica Regularization for Voxel Selection of fMRI Data," International Journal of Signal Processing Systems, Vol. 8, No. 2, pp. 32-41, June 2020. doi: 10.18178/ijsps.8.2.32-41

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