This one-of-a-kind resource provides a very readable description of the methods used for image reconstruction in magnetic resonance imaging, X-ray computed tomography, and single photon emission computed tomography. The goal of this fascinating work is to provide radiologists with a practical introduction to mathematical methods so that they may better understand the potentials and limitations of the images used to make diagnoses. Presented in four parts, this state-of-the-art text covers (1) an introduction to the models used in reconstruction, (2) an explanation of the Fourier transform, (3) a brief description of filtering, and (4) the application of these methods to reconstruction. In order to provide a better understanding of the reconstruction process, this comprehensive volume draws analogies between several different reconstruction methods. This informative reference is an absolute must for all radiology residents, as well as graduate students and professionals in the fields of physics, nuclear medicine, and computer-assisted tomography.

part |190 pages

System Models

chapter 1|6 pages


chapter 2|20 pages

Review of Basic Concepts

chapter 3|14 pages


chapter 4|10 pages


chapter 5|8 pages


chapter 6|20 pages

Complex Numbers

chapter 7|16 pages

Differential Equations

chapter 8|20 pages

Linear Algebra

chapter 9|18 pages

Linear Algebra Description of Systems

chapter 10|16 pages

Random Variables

chapter 11|10 pages

Stochastic Processes

chapter 12|22 pages

Linear, Least Mean Square Estimation

chapter 13|8 pages

Summary of System Models

part II|124 pages


chapter 14|18 pages

Introduction to the Fourier Transform

chapter 15|12 pages

Fourier Transform

chapter 16|24 pages

Properties of the Fourier Transform

chapter 17|10 pages

Polynomial Transform

chapter 18|14 pages

Discrete Fourier Transform

chapter 19|16 pages

Vector Space Rotation

chapter 20|18 pages

Other Transforms

chapter 21|10 pages

Summary of Transformations

part III|94 pages


chapter 22|18 pages

Introduction to Filtering

chapter 23|16 pages


chapter 24|14 pages

Filtering Stochastic Processes

chapter 25|16 pages

Normal Equations

chapter 26|14 pages

Wiener Filtering

chapter 27|8 pages

Image Enhancement

chapter 28|6 pages

Summary of Filtering