Dynamic MRI (Magnetic Resonance Imaging) Reconstruction as a Moment Problem. Part 1. The Beating Heart: A Problem Formulation

摘要

The paper deals with some mathematical aspects of magnetic resonance imaging (MRI) concerning the beating heart. MRI is used in diagnostic medicine to measure and display the cross section of a human organ. Some of the basic theory behind magnetic resonance is given. The author describes how a cross section of a beating human heart is measured in practice and how the measurements are arranged before an image can be made. The technique is called retrospective synchronization. If the beating heart is measured and displayed with help of this method, artefacts often deteriorate the image quality. Some of these artefacts have a physical cause, while others are caused by the reconstruction algorithm. Perhaps mathematical techniques may be used to improve these algorithms which are currently used in practice. The aim of the paper is not to solve problems, but to give an adequate mathematical formulation of the inversion problem concerning retrospective synchronization.