Medical Imaging Signals and Systems

Citation

Prince, J. L., & Links, J. M. (2015). Medical Imaging Signals and Systems (2nd ed.). Pearson.

Chapter Summary

The book has thirteen chapters in five parts, in roughly 500 pages. After a first part on principles, each modality gets a physics chapter followed by one or two chapters on its imaging systems, and the chapters end with a summary section.

Part I: Basic Imaging Principles (Chapters 1–3)

Chapter 1, "Introduction", gives a history of medical imaging, the physical signals used, and short previews of projection radiography, computed tomography, nuclear medicine, ultrasound and magnetic resonance imaging, along with multimodality imaging.

Chapter 2, "Signals and Systems", is the mathematical foundation. It covers point and line impulses, comb and sampling functions, rect and sinc functions and separable and periodic signals; linear shift-invariant systems and their impulse responses; the Fourier transform and its properties (including convolution, scaling, rotation and Parseval's theorem); the transfer function; and circular symmetry with the Hankel transform.

Chapter 3, "Image Quality", develops the measures used in every later chapter: contrast and modulation transfer function, resolution (line spread function, full width at half maximum, cascaded subsystems), noise (random variables) and signal-to-noise ratio, sampling and the Nyquist theorem, artifacts and distortion, and quantitative and diagnostic accuracy.

Part II: Radiographic Imaging (Chapters 4–6)

Chapter 4, "Physics of Radiography", covers ionization, forms of ionizing radiation, the interaction and attenuation of X-rays and the quantities used in radiation dosimetry. Chapter 5, "Projection Radiography", treats instrumentation (tubes, filtration, grids, film-screen detectors, image intensifiers, digital radiography and mammography), image formation through a basic imaging equation with geometric and blurring effects, and noise and scattering. Chapter 6, "Computed Tomography", covers CT instrumentation across generations, then image formation: line integrals, CT numbers, parallel-ray, fan-beam, helical and cone-beam reconstruction, iterative reconstruction, and image quality in terms of resolution, noise and artifacts.

Part III: Nuclear Medicine Imaging (Chapters 7–9)

Chapter 7, "The Physics of Nuclear Medicine", covers radioactive decay and its laws and modes, the statistics of decay and radiotracers. Chapter 8, "Planar Scintigraphy", describes the Anger camera (collimators, scintillation crystal, photomultiplier tubes, positioning logic), its imaging equation and image quality factors such as resolution, sensitivity, uniformity and noise. Chapter 9, "Emission Computed Tomography", covers SPECT and PET instrumentation and image formation, iterative reconstruction, and image quality including attenuation, scatter and random coincidences.

Part IV: Ultrasound Imaging (Chapters 10–11)

Chapter 10, "The Physics of Ultrasound", begins with the wave equation, then wave propagation (reflection, refraction, attenuation, scattering, nonlinear propagation), the Doppler effect and beam pattern formation and focusing. Chapter 11, "Ultrasound Imaging Systems", covers transducers and probes, the pulse-echo equation, A-, M- and B-mode scans, steering and focusing with beamforming, three-dimensional imaging, resolution, noise and speckle.

Part V: Magnetic Resonance Imaging (Chapters 12–13)

Chapter 12, "Physics of Magnetic Resonance", develops micro- and macroscopic magnetization, precession at the Larmor frequency, RF excitation, relaxation, the Bloch equations, spin echoes and basic contrast mechanisms. Chapter 13, "Magnetic Resonance Imaging", covers system components (magnet, gradient coils, RF coils), data acquisition with slice selection, frequency and phase encoding and realistic pulse sequences, image reconstruction, image quality and advanced contrast mechanisms.

Key Concepts

Part I: Basic Imaging Principles

• Linear shift-invariant systems and the Fourier transform: the toolkit used to model every imaging system in the book.
• Modulation transfer function and resolution: how a system's response to spatial frequency describes blur.
• Signal-to-noise ratio and sampling: noise measures and the Nyquist sampling theorem.

Parts II–III: Radiographic and nuclear medicine imaging

• Attenuation and the basic imaging equation: how X-ray transmission becomes a projection image.
• Reconstruction from projections: parallel-ray, fan-beam and iterative methods for CT and emission tomography.
• Radioactive decay and the Anger camera: the physics and imaging equation of scintigraphy.

Parts IV–V: Ultrasound and magnetic resonance imaging

• Pulse-echo imaging and beamforming: how echoes are timed, steered and focused into an image.
• Larmor precession, relaxation and the Bloch equations: the physics of the MR signal.
• Gradient encoding: slice selection, frequency encoding and phase encoding.

Critical Analysis

Strengths

• One framework for every modality. The authors' preface states that signal processing is the fundamental viewpoint, and the contents show the same sequence repeated: physics, instrumentation, image formation, image quality. This lets the student carry the same mathematics from one modality to the next.
• Image quality built in. Chapter 3 introduces contrast, resolution, noise and accuracy in general terms, and these topics reappear in the quality sections within the radiography, CT, nuclear medicine, ultrasound and MRI chapters, as the preface describes.
• Clearly organised for teaching. The authors report using drafts for a one-semester upper-level or graduate course at Johns Hopkins and suggest Parts I–III and IV–V as a two-semester split. Each chapter ends with a summary, and the publisher advertises motivational example problems and a wealth of images and diagrams, including biologically relevant ones.
• Mathematical depth where it matters. The contents list derivations such as the Bloch equations, the pulse-echo equation, the Anger-camera imaging equation and parallel-ray and fan-beam CT reconstruction.

Limitations

• Demanding prerequisites. The publisher describes it as most appropriate for engineering students who have taken the prerequisite signals and systems courses and elementary probability, and the authors' preface adds freshman physics, chemistry and calculus. Students without a signals course will need to study Chapter 2 carefully or take that course first.
• Physics and biology kept minimal. The preface says coverage focuses on signals and includes only enough physics and biology to motivate each modality and provide a model for analysis. Clinical practice, diagnosis and equipment details are not the focus.
• Limited scope. The contents cover five modalities and end with MRI. There is no chapter on image analysis, segmentation or visualization, and multimodality imaging appears only in the introduction. No independent reviews of the second edition were found.

Where It Fits in the Course

Prince and Links is the signals-and-systems treatment of medical imaging in this course list. Suetens's Fundamentals of Medical Imaging is a shorter, heavily illustrated survey of the same modalities that also covers image computing and visualization and sets its mathematics in skippable paragraphs; it is a lighter first pass, while Prince and Links is the better choice when the course is built on signal processing. Smith and Webb's Introduction to Medical Imaging is a compact introduction to the main clinical modalities, and Wolbarst and colleagues' Medical Imaging: Essentials for Physicians is a conceptual introduction written for readers who will use images rather than build scanners.

The Essential Physics of Medical Imaging is a comprehensive reference for radiology residents and medical physicists, with more clinical and radiation-protection content than Prince and Links. Barrett and Myers's Foundations of Image Science is the graduate treatment of the mathematics, statistics and task-based assessment of imaging systems, and a natural continuation after the image quality chapter and signal framework here.

How to Use This Book

The book suits upper-level undergraduates and first-year graduate students in biomedical or electrical engineering who have taken a signals and systems course. Work through Chapters 2 and 3 carefully, since every later chapter reuses their notation and quality measures. Then take the modalities in the book's order or by interest; within each, read the physics chapter before the imaging-systems chapter and try to derive the image equation yourself.

For a one-semester course, the authors say they skip some material and move briskly. A reasonable selection is Part I, the radiography and CT chapters, and one or two of nuclear medicine, ultrasound and MRI; Parts IV and V are natural for a second term. Use the end-of-chapter summaries to check what is essential, and work the example problems.