Inverse Fourier transformation of combined first order derivative and intensity-curvature functional of magnetic resonance angiography of the human brain

Abstract

Background and objectiveThis paper reports a novel image processing technique based on inverse Fourier transformation and its validation procedure. MethodsMagnetic Resonance Angiography (MRA) data of the human brain is fitted on a pixel-by-pixel basis with bivariate linear model polynomial function. Polynomial fitting allows the formulation of two measures: the first order derivative (FOD), which is an edge finder, and the intensity-curvature functional (ICF), which is a high pass filter. The calculation of FOD and ICF uses knowledge provided by existing research and is performed through resampling. ICF and FOD are direct Fourier transformed, and their k-space is combined through a nonlinear convolution of terms. The resulting k-space is inverse Fourier transformed so to obtain a novel image called Fourier Convolution Image (FCI). ResultsFCI possesses the characteristics of an edge finder (FOD) and a high pass filter (ICF). ConclusionsFC images yield the following properties versus MRA: 1. Change of the contrast; 2. Increased sharpness in the proximity of human brain vessels; 3. Increased visualization of vessel connectivity. The implication of this study is to provide FCI as another viable option for MRA evaluation.