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In this paper, the task-related fMRI problem is treated in its matrix factorization formulation, focused on the Dictionary Learning (DL) approach. The new method allows the incorporation of a priori knowledge associated both with the experimental design as well as with available brain Atlases. Moreover, the proposed method can efficiently cope with uncertainties related to the HRF modeling. In addition, the proposed method bypasses one of the major drawbacks that are associated with DL methods; that is, the selection of the sparsity-related regularization parameters. In our formulation, an alternative sparsity promoting constraint is employed, that bears a direct relation to the number of voxels in the spatial maps. Hence, the related parameters can be tuned using information that is available from brain atlases. The proposed method is evaluated against several other popular techniques, including GLM. The obtained performance gains are reported via a novel realistic synthetic fMRI dataset as well as real data that are related to a challenging experimental design., Comment: 46 pages, 19 figures, Complete Study of the IADL algorithm on both synthetic and real fMRI data