Riccati-regularized Precision Matrices for Neuroimaging

TL;DR

This paper explores Riccati-regularized precision matrices as an alternative to sparse connectivity graphs in neuroimaging, demonstrating their advantages in analyzing cortical maps and extracting functional biomarkers from fMRI data.

Contribution

It introduces Riccati regularized precision matrices for neuroimaging analysis, highlighting their benefits and potential to complement existing sparse methods.

Findings

Effective in analyzing cortical thickness maps

Improves extraction of functional biomarkers from fMRI

Speed and quality enhanced with random projections

Abstract

The introduction of graph theory in neuroimaging has pro- vided invaluable tools for the study of brain connectivity. These methods require the definition of a graph, which is typically derived by estimating the effective connectivity between brain regions through the optimization of an ill-posed inverse problem. Considerable efforts have been devoted to the development of methods extracting sparse connectivity graphs. The present paper aims at highlighting the benefits of an alternative ap- proach. We investigate low-rank L2 regularized matrices recently intro- duced under the denomination of Riccati regularized precision matrices. We demonstrate their benefits for the analysis of cortical thickness map and for the extraction of functional biomarkers from resting state fMRI scans. In addition, we explain how speed and result quality can be further improved with random projections. The promising results obtained using the Human Connectome Project dataset as well as the numerous possi- ble extensions and applications suggest that Riccati precision matrices might usefully complement current sparse approaches.