Learning dictionaries from correlated data: Application to fMRI data analysis

Abstract

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 (ICA) for functional magnetic resonance imaging (fMRI) data analysis. fMRI data sets are however structured data matrices with notions of spatio-temporal correlation. This prior information has not been included in the K-SVD algorithm when applied in fMRI data analysis. In this paper we remedy to this situation by proposing a variant of the K-SVD algorithm dedicated to fMRI data analysis by taking into account this prior information. The proposed algorithm accounts for the known correlation structure in the fMRI data by using the squared Q, R-norm instead of the Frobenius norm for rank one approximation in the dictionary update stage. The performance of the proposed algorithm is illustrated through simulations and applications on a real fMRI data set.