Discovering functional connectivity between and within brain regions is a key concern in neuroscience. Due to the noise inherent in fMRI data, it is challenging to characterize the properties of individual voxels, and current methods are unable to flexibly analyze voxel-level connectivity differences. We propose a new functional connectivity method which incorporates a spatial smoothness constraint using regularized optimization, enabling the discovery of voxel-level interactions between brain regions from the small datasets characteristic of fMRI experiments. We validate our method in two separate experiments, demonstrating that we can learn coherent connectivity maps that are consistent with known results. First, we examine the functional connectivity between early visual areas V1 and VP, confirming that this connectivity structure preserves retinotopic mapping. Then, we show that two category-selective regions in ventral cortex - the Parahippocampal Place Area (PPA) and the Fusiform Face Area (FFA) - exhibit an expected peripheral versus foveal bias in their connectivity with visual area hV4. These results show that our approach is powerful, widely applicable, and capable of uncovering complex connectivity patterns with only a small amount of input data.
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