Pulse-transfer function of the intensity-curvature functional: Applications in magnetic resonance angiography of the human brain

Abstract

This paper reports additional evidence of the high-pass filtering properties of the intensity-curvature functional (ICF). Magnetic resonance angiography (MRA) of the human brain is used to calculate its ICF. MRA and ICF are direct Z-transformed. The pulsetransfer function (PTF) of the ICF is defined as the inverse Z-transform of the ratio between Z-space of ICF and Z-space of MRA. The image space of PTF is calculated and is direct Z-transformed. MRA is reconstructed through inverse Z-transform of the ratio between Z-space of ICF and Z-space of PTF. MRA reconstruction proves correctness of the approximated approach and adds evidence to the assumption that ICF is a high-pass filter. This research provides two novelties: (1) additional evidence that ICF is a high-pass filter and (2) a medical image processing technique that proves correct that the PTF of a high-pass filter (ICF) can be approximated by the ratio between Z-space of ICF and Z-space of MRA. It follows that MRA can be reconstructed using the inverse Z-transform of the ratio between Z-space of ICF and Z-space of PTF.