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This book provides a firm foundation in the mathematical tools used to model the measurements at the heart of medical imaging technology, and now includes a.
Table of contents
- Medical imaging: tomography and 3D reconstruction
- Medical imaging: tomography and 3D reconstruction - ENSIMAG
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Contents 1. Measurements and Modeling. Linear Models and Linear Equations. A Basic Model for Tomography. Introduction to the Fourier Transform. The Radon Transform. Introduction to Fourier Series.
Implementing Shift Invariant Filters. Reconstruction in x-ray Tomography.
Medical imaging: tomography and 3D reconstruction
Imaging Artifacts in x-ray Tomography. It also has a nice section on algebraic reconstruction techniques, as they are illustrative of interesting mathematics, even if not widely used in modern practice. This book is valuable, for it addresses with care and rigor the relevance of a variety of mathematical topics to a real-world problem.
I intend to add this book to the list of supplemental readings for my medical physics students, as it should reduce the frustration of my mathematically sophisticated students who could benefit from this text's careful treatment of topics that I present only verbally, conceptually, and with great waving of hands. I have only a few quibbles with the book. One minor point is that the reader is led to infer that all random processes are zero-mean.
Another is some statements made in passing that imply that helical scanning and cone beam geometry in CT inherently reduce the patient dose by faster data acquisition as if the patient dose were solely a consequence of the beam-on time. The author repeats the common assertion that twice rather than strictly greater than twice the maximum frequency of a band-limited signal is an adequate uniform sampling rate.
The book says little about noise and statistics and even less about the treatment of nonideal conditions such as beam-hardening effects in CT and attenuation, scatter, and spatially variable resolution effects in SPECT and PET.
Medical imaging: tomography and 3D reconstruction - ENSIMAG
Other than Kaczmarz's method for algebraic reconstruction, iterative reconstruction is not developed. These absences are hardly defects, given the introductory purpose of the book and its brevity. Presenting MRI in a single chapter is a daunting task, and the chapter on MRI works all the way up to 1-dimensional frequency encoding only to end abruptly.
Within a few more pages, the view of the raw data from 2-dimensional MRI as the Fourier transform of the image plane could have been developed and then tied through the Central Slice Theorem to reconstruction in PET, SPECT, and CT, thereby connecting the modalities and unifying the topics of the book. This book is well written. New Releases. Introduction to the Mathematics of Medical Imaging. Description At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data.
This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most of these modalities. The text uses X-ray computed tomography X-ray CT as a 'pedagogical machine' to illustrate important ideas and its extensive discussion of background material makes the more advanced mathematical topics accessible to people with a less formal mathematical education. This new edition contains a chapter on magnetic resonance imaging MRI , a revised section on the relationship between the continuum and discrete Fourier transforms, an improved description of the gridding method, and new sections on both Grangreat's formula and noise analysis in MR-imaging.
Mathematical concepts are illuminated with over illustrations and numerous exercises. Table of contents Preface to the second edition; Preface; How to use this nook; Notational conventions; 1. Measurements and modeling; 2. Linear models and linear equations; 3.
A basic model for tomography; 4. Introduction to the Fourier transform; 5. Convolution; 6. The radon transform; 7.
Introduction to Fourier series; 8.