Multi-Parametric MR Image Processing using Higher Dimensional Vector Algebra

Dawit Assefa, Harry Keller, and David A. Jaffray


Magnetic Resonance Imaging (MRI), Medical Image Processing, Multi Parametric, Quaternion, Trinion


In this preliminary analysis, multi parametric Magnetic Resonance Images (MRI) are expressed as two dimensional multi component (color) signals in higher order algebraic spaces. Traditionally, each component of such images is analyzed serially. Such an approach however has a main drawback in that it misses the information as to how the different parameters are correlated to each other. In this study, building upon a recent application in color image processing, themultipleMR parameters are combined to one entity and analyzed holistically using higher order Fourier transforms. The approach has been implemented in terms of classifying structures in MR images taken from a cohort of patients treated for glioblastoma multiforme. Our results show that, as opposed to a serial analysis, a holistic use of the inter correlation information embedded among individual parameters may be vital in detecting signals of interest that are not readily available.

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