Fast and robust FMRI unmixing using hierarchical dictionary learning

We propose a novel computationally efficient hierarchical dictionary learning (HDL) approach for data-driven unmixing and functional connectivity analysis of functional magnetic resonance imaging (fMRI) data. It is shown that by simultaneously exploiting the sparsity of the spatial brain maps and the incoherence among their evolution in time or task functions, one can achieve better performance while overcoming the drawbacks of existing approaches. The task functions constituting the dictionary, are learned using a hierarchical subset selection approach. Here, to enforce incoherence among atoms, any new atom is selected from suitable training candidates if it does not lie in the column span of past selected atoms. Also, since the sparsity of spatial maps is generally unknown and affected due to acquisition artifacts, HDL doesn't make use of an implicit sparse coding stage while dictionary update. This makes HDL a very fast and efficient data-driven approach for fMRI analysis. Experimental results on synthetic and real fMRI datasets provide compelling evidences that HDL performs better than existing state-of-the-art methods.