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9780130653536

Medical Imaging Signals And Systems

by ;
  • ISBN13:

    9780130653536

  • ISBN10:

    0130653535

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2005-04-15
  • Publisher: Prentice Hall
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Summary

This book has developed over the past 14 years, during which time we have taught a course on medical imaging systems at Johns Hopkins University. This course started out as a survey course, and then evolved according to our mutual interests and inclinations into a course that emphasizes the signals and systems aspects—or more precisely, the signal processing aspects—of medical imaging.

With signal processing as the fundamental viewpoint, this book covers the most important imaging modalities in radiology: projection radiography, x-ray computed tomography, nuclear medicine, ultrasound imaging, and magnetic resonance imaging. The authors expect the reader to be familiar with signals and systems, which are usually covered in the sophomore year of most engineering curricula, and with elementary probability. Freshman courses in physics, chemistry, and calculus are also assumed.

The book is organized into parts emphasizing key overall conceptual divisions, as follows. Part I introduces basic imaging principles, including an introduction to medical imaging systems in Chapter 1, a review of signal processing in Chapter 2 (with emphasis on two-dimensional signals), and a discussion of image quality in Chapter 3. Our presentation of the theory of medical imaging systems is strongly based on continuous signals; however, a development of discrete signals is included to permit discussions on sampling and implementation. Issues of image quality, including resolution, noise, contrast, geometric distortion, and artifacts are described in general context here, but revisited within each modality in subsequent chapters.

Part II describes key modalities in radiographic imaging. It begins in Chapter 4 with a brief presentation of the physics of radiography, including the generation and detection of ionizing radiation and its effect on the human body. Chapter 5 describes projection radiography systems, including chest x-ray and fluoroscopy systems. As in all subsequent chapters, coverage focuses on signals, including only enough physics and biology to motivate the modality and provide a model for the analysis. Chapter 5 also presents the mathematics of projection imaging, a very fundamental idea in medical imaging. Chapters 6 covers x-ray computed tomography, expanding on the instrumentation and mathematics of projection imaging and introducing the concept of image reconstruction in medical imaging. Computed tomography produces true tomograms (images of cross sections of the body) rather than projections of the body.

Part IV presents the physics and modalities of nuclear medicine imaging. Chapter 7 describes the physics of nuclear medicine, focusing primarily on the concept of radioactivity. The major modalities in nuclear medicine imaging are described in Chapter 8, which covers planar scintigraphy, and Chapter 9, which covers emission computed tomography.

Part IV covers ultrasound imaging. It begins in Chapter 10 with a brief presentation of the physics of sound, and continues in Chapter 11 with the various imaging modes offered within this rich modality. Part V covers magnetic resonance imaging. Chapter 11 presents the physics of nuclear magnetic resonance, and Chapter 12 continues with a presentation of various magnetic resonance imaging techniques.

We have used drafts of this book for a one-semester upper-level/graduate course on medical imaging systems. In order to cover the material in one semester, we routinely skip some material in the book and we move at a very brisk pace. We feel that this book could be used in a two-semester course as well, perhaps by covering Parts I-III in the first semester and Parts IV-V in the second semester. A two-semester approach would allow instructors to use supplementary materials for additional depth or to present current research topics.

Medical imaging is very visual—just ask any radiologist. Although the formalism of signals and systems is mathematical, we understand the advantages offered through visualization. Therefore, the book contains many images and diagrams. Some are strictly pedagogical, offered in conjunction with the exposition or an example problem. Others are motivational, 'revealing interesting features for discussion or study. Special emphasis is made to provide biologically relevant examples including images, so that the important context of medical imaging can be appreciated by students.

Many students, friends, colleagues, and teaching assistants contributed to this book through discussions and critiques. Xiao Han, Li Pan, and Vijay Parthasarathy contributed problems and solutions, and Aaron Carass fixed many LaTeX and CVS problems. A special note of appreciation is due to Xiaodong Tao, who created and solved many of the examples and problems. We would also like to thank Rama Chellappa, Brian Caffo, and Sarah Ying, who provided comments and suggestions on several parts of the book. We also thank William R. Brody, who inspired the creation of the course out of which this book grew and who also wrote one of the chapters in our original course notes. Finally, we convey special thanks to Elliot R. McVeigh and John I. Goutsias, who co-taught our course at Hopkins during the early years and helped draft the original version of this book.

JERRY L. PRINCE
JONATHAN M. LINKS

Table of Contents

Preface xv
Part I Basic Imaging Principles
1(102)
Overview
1(4)
Introduction
5(10)
History of Medical Imaging
5(1)
Physical Signals
6(1)
Imaging Modalities
7(1)
Projection Radiography
8(1)
Computed Tomography
9(1)
Nuclear Medicine
10(1)
Ultrasound Imaging
11(1)
Magnetic Resonance Imaging
12(1)
Summary and Key Concepts
13(2)
Signals and Systems
15(48)
Introduction
15(1)
Signals
16(8)
Point Impulse
16(3)
Line Impulse
19(1)
Comb and Sampling Functions
19(1)
Rect and Sinc Functions
20(2)
Exponential and Sinusoidal Signals
22(1)
Separable Signals
23(1)
Periodic Signals
23(1)
Systems
24(8)
Linear Systems
24(1)
Impulse Response
25(1)
Shift Invariance
26(2)
Connections of LSI Systems
28(2)
Separable Systems
30(2)
Stable Systems
32(1)
The Fourier Transform
32(5)
Properties of the Fourier Transform
37(6)
Linearity
37(1)
Translation
37(2)
Conjugation and Conjugate Symmetry
39(1)
Scaling
39(1)
Rotation
40(1)
Convolution
40(1)
Product
41(1)
Separable Product
41(1)
Parseval's Theorem
42(1)
Separability
42(1)
Transfer Function
43(2)
Circular Symmetry and the Hankel Transform
45(4)
Sampling
49(6)
Sampling Signal Model
50(2)
Nyquist Sampling Theorem
52(2)
Anti-Aliasing Filters
54(1)
Summary and Key Concepts
55(8)
Image Quality
63(40)
Introduction
63(1)
Contrast
64(6)
Modulation
65(1)
Modulation Transfer Function
65(4)
Local Contrast
69(1)
Resolution
70(8)
Line Spread Function
70(2)
Full Width at Half Maximum
72(1)
Resolution and Modulation Transfer Function
72(3)
Subsystem Cascade
75(2)
Resolution Tool
77(1)
Temporal and Spectral Resolution
78(1)
Noise
78(8)
Random Variables
79(1)
Continuous Random Variables
80(2)
Discrete Random Variables
82(2)
Independent Random Variables
84(2)
Signal-to-Noise Ratio
86(4)
Amplitude SNR
86(1)
Power SNR
87(2)
Differential SNR
89(1)
Nonrandom Effects
90(2)
Artifacts
90(1)
Distortion
91(1)
Accuracy
92(3)
Quantitative Accuracy
92(1)
Diagnostic Accuracy
93(2)
Summary and Key Concepts
95(8)
Part II Radiographic Imaging
103(130)
Overview
103(3)
Physics of Radiography
106(29)
Introduction
106(1)
Ionization
107(3)
Atomic Structure
107(1)
Electron Binding Energy
108(1)
Ionization and Excitation
109(1)
Forms of Ionizing Radiation
110(3)
Particulate Radiation
110(2)
Electromagnetic Radiation
112(1)
Nature and Properties of Ionizing Radiation
113(8)
Primary Energetic Electron Interactions
114(2)
Primary Electromagnetic Radiation Interactions
116(5)
Attenuation of Electromagnetic Radiation
121(7)
Measures of X-Ray Beam Strength
121(2)
Narrow Beam, Monoenergetic Photons
123(3)
Narrow Beam, Polyenergetic Photons
126(1)
Broad Beam Case
127(1)
Radiation Dosimetry
128(3)
Exposure
128(1)
Dose and Kerma
129(1)
Linear Energy Transfer
129(1)
The f-Factor
129(1)
Dose Equivalent
130(1)
Effective Dose
131(1)
Summary and Key Concepts
131(4)
Projection Radiography
135(46)
Introduction
135(1)
Instrumentation
136(14)
X-Ray Tubes
136(3)
Filtration and Restriction
139(2)
Compensation Filters and Contrast Agents
141(3)
Grids, Airgaps, and Scanning Slits
144(2)
Film-Screen Detectors
146(2)
X-Ray Image Intensifiers
148(2)
Image Formation
150(14)
Basic Imaging Equation
150(1)
Geometric Effects
150(8)
Blurring Effects
158(4)
Film Characteristics
162(2)
Noise and Scattering
164(7)
Signal-to-Noise Ratio
164(3)
Quantum Efficiency and Detective Quantum Efficiency
167(2)
Compton Scattering
169(2)
Summary and Key Concepts
171(10)
Computed Tomography
181(52)
Introduction
181(2)
CT Instrumentation
183(9)
CT Generations
183(6)
X-Ray Source and Collimation
189(1)
CT Detectors
190(1)
Gantry, Slip Ring, and Patient Table
191(1)
Image Formation
192(17)
Line Integrals
192(1)
CT Numbers
193(1)
Parallel-Ray Reconstruction
193(11)
Fan-Beam Reconstruction
204(3)
Helical CT Reconstruction
207(1)
Cone Beam CT
208(1)
Image Quality in CT
209(9)
Resolution
209(3)
Noise
212(5)
Artifacts
217(1)
Summary and Key Points
218(15)
Part III Nuclear Medicine Imaging
233(80)
Overview
233(4)
The Physics of Nuclear Medicine
237(15)
Introduction
237(1)
Nomenclature
237(1)
Radioactive Decay
238(5)
Mass Defect and Binding Energy
238(2)
Line of Stability
240(1)
Radioactivity
240(1)
Radioactive Decay Law
241(2)
Modes of Decay
243(1)
Positron Decay and Electron Capture
243(1)
Isomeric Transition
244(1)
Statistics of Decay
244(2)
Radiotracers
246(3)
Summary and Key Concepts
249(3)
Planar Scintigraphy
252(34)
Introduction
252(1)
Instrumentation
252(9)
Collimators
253(2)
Scintillation Crystal
255(1)
Photomultiplier Tubes
255(2)
Positioning Logic
257(1)
Pulse Height Analyzer
258(1)
Gating Circuit
259(1)
Image Capture
260(1)
Image Formation
261(8)
Event Position Estimation
261(2)
Acquisition Modes
263(3)
Anger Camera Imaging Equation
266(3)
Image Quality
269(10)
Resolution
269(3)
Sensitivity
272(3)
Uniformity
275(1)
Energy Resolution
275(1)
Noise
276(2)
Factors Affecting Count Rate
278(1)
Summary and Key Concepts
279(7)
Emission Computed Tomography
286(27)
Instrumentation
287(7)
SPECT Instrumentation
287(2)
PET Instrumentation
289(5)
Image Formation
294(10)
SPECT Image Formation
295(3)
PET Image Formation
298(5)
Iterative Reconstruction
303(1)
Image Quality in SPECT and PET
304(4)
Spatial Resolution
304(1)
Attenuation and Scatter
305(2)
Random Coincidences
307(1)
Contrast
308(1)
Noise and Signal-to-Noise
308(1)
Summary and Key Concepts
308(5)
Part IV Ultrasound Imaging
313(66)
Overview
313(2)
The Physics of Ultrasound
315(32)
Introduction
315(1)
The Wave Equation
316(6)
Three-Dimensional Acoustic Waves
317(2)
Plane Waves
319(2)
Spherical Waves
321(1)
Wave Propagation
322(6)
Acoustic Energy and Intensity
322(1)
Reflection and Refraction at Plane Interfaces
323(1)
Transmission and Reflection Coefficients at Plane Interfaces
324(1)
Attenuation
325(3)
Scattering
328(1)
Doppler Effect
328(5)
Beam Pattern Formation and Focusing
333(9)
Simple Field Pattern Model
333(1)
Diffraction Formulation
334(7)
Focusing
341(1)
Summary and Key Concepts
342(5)
Ultrasound Imaging Systems
347(32)
Introduction
347(1)
Instrumentation
347(6)
Ultrasound Transducer
347(3)
Ultrasound Probes
350(3)
Pulse-Echo Imaging
353(3)
The Pulse-Echo Equation
353(3)
Transducer Motion
356(3)
Ultrasound Imaging Modes
359(6)
A-Mode Scan
359(1)
M-Mode Scan
360(1)
B-Mode Scan
360(5)
Steering and Focusing
365(6)
Transmit Steering and Focusing
366(2)
Beamforming and Dynamic Focusing
368(3)
Three-Dimensional Ultrasound Imaging
371(1)
Summary and Key Concepts
371(8)
Part V Magnetic Resonance Imaging
379(86)
Overview
379(2)
Physics of Magnetic Resonance
381(28)
Introduction
381(1)
Microscopic Magnetization
381(2)
Macroscopic Magnetization
383(2)
Precession and Larmor Frequency
385(2)
Transverse and Longitudinal Magnetization
387(3)
NMR Signals
388(2)
Rotating Frame
390(1)
RF Excitation
390(3)
Relaxation
393(3)
The Bloch Equations
396(1)
Spin Echoes
397(3)
Contrast Mechanisms
400(3)
Summary and Key Concepts
403(6)
Magnetic Resonance Imaging
409(56)
Instrumentation
409(8)
System Components
409(1)
Magnet
410(2)
Gradient Coils
412(3)
Radio-Frequency Coils
415(1)
Scanning Console and Computer
416(1)
MRI Data Acquisition
417(24)
Encoding Spatial Position
417(2)
Slice Selection
419(6)
Frequency Encoding
425(5)
Polar Scanning
430(1)
Gradient Echoes
431(2)
Phase Encoding
433(2)
Spin Echoes
435(2)
Pulse Repetition Interval
437(1)
Realistic Pulse Sequences
438(3)
Image Reconstruction
441(5)
Rectilinear Data
441(1)
Polar Data
442(1)
Imaging Equations
443(3)
Image Quality
446(9)
Sampling
446(2)
Resolution
448(3)
Noise
451(2)
Signal-to-Noise Ratio
453(1)
Artifacts
454(1)
Summary and Key Concepts
455(10)
Index 465

Supplemental Materials

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Excerpts

This book has developed over the past 14 years, during which time we have taught a course on medical imaging systems at Johns Hopkins University. This course started out as a survey course, and then evolved according to our mutual interests and inclinations into a course that emphasizes thesignals and systemsaspects--or more precisely, the signal processing aspects--of medical imaging.With signal processing as the fundamental viewpoint, this book covers the most importantimaging modalitiesin radiology: projection radiography, x-ray computed tomography, nuclear medicine, ultrasound imaging, and magnetic resonance imaging. The authors expect the reader to be familiar with signals and systems, which are usually covered in the sophomore year of most engineering curricula, and with elementary probability. Freshman courses in physics, chemistry, and calculus are also assumed.The book is organized into parts emphasizing key overall conceptual divisions, as follows. Part I introduces basic imaging principles, including an introduction to medical imaging systems in Chapter 1, a review of signal processing in Chapter 2 (with emphasis on two-dimensional signals), and a discussion of image quality in Chapter 3. Our presentation of the theory of medical imaging systems is strongly based on continuous signals; however, a development of discrete signals is included to permit discussions on sampling and implementation. Issues of image quality, including resolution, noise, contrast, geometric distortion, and artifacts are described in general context here, but revisited within each modality in subsequent chapters.Part II describes key modalities in radiographic imaging. It begins in Chapter 4 with a brief presentation of the physics of radiography, including the generation and detection of ionizing radiation and its effect on the human body. Chapter 5 describes projection radiography systems, including chest x-ray and fluoroscopy systems. As in all subsequent chapters, coverage focuses on signals, including only enough physics and biology to motivate the modality and provide a model for the analysis. Chapter 5 also presents the mathematics of projection imaging, a very fundamental idea in medical imaging. Chapters 6 covers x-ray computed tomography, expanding on the instrumentation and mathematics ofprojection imagingand introducing the concept of image reconstruction in medical imaging. Computed tomography produces truetomograms(images of cross sections of the body) rather than projections of the body.Part IV presents the physics and modalities of nuclear medicine imaging. Chapter 7 describes the physics of nuclear medicine, focusing primarily on the concept of radioactivity. The major modalities in nuclear medicine imaging are described in Chapter 8, which covers planar scintigraphy, and Chapter 9, which covers emission computed tomography.Part IV covers ultrasound imaging. It begins in Chapter 10 with a brief presentation of the physics of sound, and continues in Chapter 11 with the various imaging modes offered within this rich modality. Part V covers magnetic resonance imaging. Chapter 11 presents the physics of nuclear magnetic resonance, and Chapter 12 continues with a presentation of various magnetic resonance imaging techniques.We have used drafts of this book for a one-semester upper-level/graduate course on medical imaging systems. In order to cover the material in one semester, we routinely skip some material in the book and we move at a very brisk pace. We feel that this book could be used in a two-semester course as well, perhaps by covering Parts I-III in the first semester and Parts IV-V in the second semester. A two-semester approach would allow instructors to use supplementary materials for additional depth or to present current research topics.Medical imaging is very visual--just ask any radiologist. Although the formalism

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