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

This paper reports a novel image processing technique based on inverse Fourier transformation and its validation procedure. Magnetic 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). FCI possesses the characteristics of an edge finder (FOD) and a high pass filter (ICF). FC 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. Magnetic Resonance Angiography (MRA) in (a). First Order Derivative (FOD) image of MRA in (b). Intensity-Curvature Functional (ICF) image of MRA in (c). Fourier Convolution Image (FCI) of MRA in (d). FCI is obtained merging k-space of FOD and k-space of ICF and inverse Fourier transforming. FOD sharpens the vessels (see structures pointed by the arrows in (b)). This characteristic is replicated in FC image where can be noted the fusion between the dark background of FOD and the gray levels of ICF with consequent increased visibility of the vessels (see (d)) and a clear change of the contrast versus MRA. [Display omitted]