Magnetic Resonance Imaging

The Basics

Christakis Constantinides

• Editorial: CRC Press
• Año: 2016
• ISBN:
  9780429585937
• Edición: 1
• Categoría: Medicine
• Categoría: Medical Theory, Practice & Reference

Magnetic resonance imaging (MRI) is a rapidly developing field in basic applied science and clinical practice. Research efforts in this area have already been recognized with five Nobel prizes awarded to seven Nobel laureates in the past 70 years. Based on courses taught at The Johns Hopkins University, Magnetic Resonance Imaging: The Basics provid

1	Fourier Transformations

1.1 Introduction

Fourier transformation is a powerful mathematical operation. It was named after Jean Baptiste Joseph Fourier, a French mathematician and physicist (1768–1830) who initiated the investigation of Fourier series and its application to problems of heat flow. This integral transform reexpresses a function in terms of its sinusoidal basis functions as a scaled summation. The advent of electronics and the evolution of computers in the early 20th century allowed computation and digital signal processing using the Fourier transform (FT) in the discrete domain.

Interestingly, in the 1960s, Professor Richard Ernst (Ernst 1966, Ernst 1987) at the ETH in Zurich applied the basic Fourier transformation in its discrete form to formulate the magnetic resonance imaging (MRI) signal evolution in pulse-acquire ...