Sequential Dictionary Learning From Correlated Data: Application to fMRI Data Analysis.

Sequential dictionary learning via the K-SVD algorithm has been revealed as a successful alternative to conventional data driven methods, such as independent component analysis for functional magnetic resonance imaging (fMRI) data analysis. fMRI data sets are however structured data matrices with notions of spatio-temporal correlation and temporal smoothness. This prior information has not been included in the K-SVD algorithm when applied to fMRI data analysis. In this paper, we propose three variants of the K-SVD algorithm dedicated to fMRI data analysis by accounting for this prior information. The proposed algorithms differ from the K-SVD in their sparse coding and dictionary update stages. The first two algorithms account for the known correlation structure in the fMRI data by using the squared Q, R-norm instead of the Frobenius norm for matrix approximation. The third and last algorithms account for both the known correlation structure in the fMRI data and the temporal smoothness. The temporal smoothness is incorporated in the dictionary update stage via regularization of the dictionary atoms obtained with penalization. The performance of the proposed dictionary learning algorithms is illustrated through simulations and applications on real fMRI data.