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Voxel selection techniques can reveal important brain regions in 3-dimensional functional magnetic resonance imaging (fMRI) data analysis. In order to counteract the contamination of noise and find meaningful voxels for fMRI analysis, the sparse representation methods like Lasso have been recently proved to be efficient for voxel selection in fMRI data. However, the voxels selected by these methods generally lose the clustering property of activated brain regions. In this work, we consider a sparse representation approach with multi-dimensional derivative constraints to detect a small portion of fMRI voxels with task relevant information. The proposed method takes into account the correlation and smoothness of activation amplitudes among neighboring voxels in cortex. Preliminary data analysis results validate the effectiveness of the proposed method.