Functional Data Analysis for Imaging Mean Function Estimation: Computing Times and Parameter Selection

Abstract

In the field of medical imaging, one of the most extended research setups consists of the comparison between two groups of images, a pathological set against a control set, in order to search for statistically significant differences in brain activity. Functional Data Analysis (FDA), a relatively new field of statistics dealing with data expressed in the form of functions, uses methodologies which can be easily extended to the study of imaging data. Examples of this have been proposed in previous publications where the authors settle the mathematical groundwork and properties of the proposed estimators. The methodology herein tested allows for the estimation of mean functions and simultaneous confidence corridors (SCC), also known as simultaneous confidence bands, for imaging data and for the difference between two groups of images. FDA applied to medical imaging presents at least two advantages compared to previous methodologies: it avoids loss of information in complex data structures and avoids the multiple comparison problem arising from traditional pixel-to-pixel comparisons. Nonetheless, computing times for this technique have only been explored in reduced and simulated setups. In the present article, we apply this procedure to a practical case with data extracted from open neuroimaging databases; then, we measure computing times for the construction of Delaunay triangulations and for the computation of mean function and SCC for one-group and two-group approaches. The results suggest that the previous researcher has been too conservative in parameter selection and that computing times for this methodology are reasonable, confirming that this method should be further studied and applied to the field of medical imaging.