Contents:

1Introduction

Introduction 1

Fundamentals of Xray Physics

Milestones of Computed Tomography

Fundamentals of Signal Processing 101

TwoDimensional FourierBased Reconstruction Methods

Algebraic and Statistical Reconstruction Methods

Technical Implementation

ThreeDimensional FourierBased Reconstruction Methods

Image Quality and Artifacts

Practical Aspects of Computed Tomography

Dose

References

Subject Index

Tis book provides an overview of X-ray technology, the historic developmental milestones of modern CT systems, and gives a comprehensive insight into the main reconstruction methods used in computed tomography. Te basis of reconstr- tion is, undoubtedly, mathematics. However, the beauty of computed tomography cannot be understood without a detailed knowledge of X-ray generation, photon– matter interaction, X-ray detection, photon statistics, as well as fundamental signal processing concepts and dedicated measurement systems. Terefore, the reader will ?nd a number of references to these basic disciplines together with a brief introd- tion to the underlying principles of CT. Tis book is structured to cover the basics of CT: from photon statistics to m- ern cone-beam systems. However, the main focus of the book is concerned with - tailed derivations of reconstruction algorithms in ?D and modern ?D cone-beam systems. A thorough analysis of CT artifacts and a discussion of practical issues, such as dose considerations, provide further insight into modern CT systems. While mainly written for graduate students in biomedical engineering, medical engine- ing science, medical physics, medicine (radiology), mathematics, electrical eng- eering, and physics, experienced practitioners in these ?elds will bene?t from this book as well. Common terms and phrases: acquisition actually already anode applied approximately artifacts attenuation axial backprojection beam calculated called circle computed cone-beam considered convolution coordinate corresponding depends derivative described detector array determined different direction discrete discussed distance distribution domain dose electron element energy equations example expression fact factor fan-beam Figure filtered Fourier transform frequency function geometry given illustrates increased integration interpolation interval inverse leads limited linear located means measured method object obtained oo oo patient photon physical pixel plane position possible practice problem projection angle radiation Radon space reconstruction represents respect result rotation sampling scan scanners scattering schematically Sect shown shows side signal simple single slice solution spatial step substituted surface term theorem thickness three-dimensional tion tomography two-dimensional unit values variable vector volume weighting window X-ray source X-ray tube