title: Complex-valued time-series correlation increases sensitivity in FMRI analysis.
abstract: To develop a linear matrix representation of correlation between complex-valued (CV) time-series in the temporal Fourier frequency domain, and demonstrate its increased sensitivity over correlation between magnitude-only (MO) time-series in functional MRI (fMRI) analysis.
  
  
  
  The standard in fMRI is to discard the phase before the statistical analysis of the data, despite evidence of task related change in the phase time-series. With a real-valued isomorphism representation of Fourier reconstruction, correlation is computed in the temporal frequency domain with CV time-series data, rather than with the standard of MO data. A MATLAB simulation compares the Fisher-z transform of MO and CV correlations for varying degrees of task related magnitude and phase amplitude change in the time-series. The increased sensitivity of the complex-valued Fourier representation of correlation is also demonstrated with experimental human data. Since the correlation description in the temporal frequency domain is represented as a summation of second order temporal frequencies, the correlation is easily divided into experimentally relevant frequency bands for each voxel's temporal frequency spectrum. The MO and CV correlations for the experimental human data are analyzed for four voxels of interest (VOIs) to show the framework with high and low contrast-to-noise ratios in the motor cortex and the supplementary motor cortex.
  
  
  
  The simulation demonstrates the increased strength of CV correlations over MO correlations for low magnitude contrast-to-noise time-series. In the experimental human data, the MO correlation maps are noisier than the CV maps, and it is more difficult to distinguish the motor cortex in the MO correlation maps after spatial processing.
  
  
  
  Including both magnitude and phase in the spatial correlation computations more accurately defines the correlated left and right motor cortices. Sensitivity in correlation analysis is important to preserve the signal of interest in fMRI data sets with high noise variance, and avoid excessive processing induced correlation.
authors.affiliation: Department of Mathematics, Statistics, and Computer Science, Marquette University, Milwaukee, WI, USA.
authors.forename: Mary C
authors.initials: MC
authors.lastname: Kociuba
authors.affiliation: Department of Mathematics, Statistics, and Computer Science, Marquette University, Milwaukee, WI, USA; Department of Biophysics, Medical College of Wisconsin, Milwaukee, WI, USA. Electronic address: daniel.rowe@marquette.edu.
authors.forename: Daniel B
authors.initials: DB
authors.lastname: Rowe
mesh_terms: D005583:Fourier Analysis; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D009044:Motor Cortex / Q000000981:diagnostic imaging*
keywords: Complex correlation; Frequency correlation; Functional magnetic resonance imaging; Magnetic resonance imaging