Robust Subject-Wise Dictionary Learning for fMRI

Abstract

This paper presents a robust subject-wise sequential dictionary learning (swsDL) algorithm named rswsDL for functional magnetic resonance imaging (fMRI) data where the negative impact of dimensionality reduction in the form of information loss and sensitivity to anomalous observations due to the assumption of Gaussian prior has been resolved by rotating the reduced dimensions to optimal direction and replacing the quadratic loss in the data fidelity term with $\alpha $ -divergence based loss function to counter the outliers, respectively. While dimensionality optimization guaranteed robustness to model order by maximizing signal intensity and smoothness, the robust loss function guaranteed decomposition stability against deviations from the Gaussian noise model. The proposed algorithm was derived by deploying spatial and temporal bases from the computationally fast sparse spatiotemporal blind source separation (ssBSS) method and solving a sequence of rank-1 matrix decomposition problems, where the $l_{1}/l_{0}$ -norm penalty/constraint promoted sparsity, and the estimation of sparse representation matrices was accomplished using a block coordinate descent approach. This strategy allowed the utilization of multi-subject fMRI data to enhance the subject-wise source separation in a robust manner. It, therefore, can be considered a promising alternative to the state-of-the-art robust consistent adaptive sequential dictionary learning (rACSD) algorithm. The rswsDL and existing robust dictionary learning based source separation algorithms were applied to synthetic and experimental fMRI datasets to validate its performance. The rswsDL algorithm manifested a 16.7% increase in the mean correlation value over the rACSD algorithm.

Keywords

• Robust subject-wise analysis
• fMRI
• sparse representation
• group-level analysis
• dictionary learning
• representation matrices