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3D Image Reconstruction for CT and PET: A Practical Guide with Python

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This is a practical guide to tomographic image reconstruction with projection data, with strong focus on Computed Tomography (CT) and Positron Emission Tomography (PET). Classic methods such as FBP, ART, SIRT, MLEM and OSEM are presented with modern and compact notation, with the main goal of guiding the reader from the comprehension of the mathematical background through a fast-route to real practice and computer implementation of the algorithms. Accompanied by example data sets, real ready-to-run Python toolsets and scripts and an overview the latest research in the field, this guide will be invaluable for graduate students and early-career researchers and scientists in medical physics and biomedical engineering who are beginners in the field of image reconstruction.

 

  • A top-down guide from theory to practical implementation of PET and CT reconstruction methods, without sacrificing the rigor of mathematical background
  • Accompanied by Python source code snippets, suggested exercises, and supplementary ready-to-run examples for readers to download from the CRC Press website
  • Ideal for those willing to move their first steps on the real practice of image reconstruction, with modern scientific programming language and toolsets

 

Daniele Panetta is a researcher at the Institute of Clinical Physiology of the Italian National Research Council (CNR-IFC) in Pisa. He earned his MSc degree in Physics in 2004 and specialisation diploma in Health Physics in 2008, both at the University of Pisa. From 2005 to 2007, he worked at the Department of Physics "E. Fermi" of the University of Pisa in the field of tomographic image reconstruction for small animal imaging micro-CT instrumentation. His current research at CNR-IFC has as its goal the identification of novel PET/CT imaging biomarkers for cardiovascular and metabolic diseases. In the field micro-CT imaging, his interests cover applications of three-dimensional morphometry of biosamples and scaffolds for regenerative medicine. He acts as reviewer for scientific journals in the field of Medical Imaging: Physics in Medicine and Biology, Medical Physics, Physica Medica, and others. Since 2012, he is adjunct professor in Medical Physics at the University of Pisa.

Niccolò Camarlinghi is a researcher at the University of Pisa. He obtained his MSc in Physics in 2007 and his PhD in Applied Physics in 2012. He has been working in the field of Medical Physics since 2008 and his main research fields are medical image analysis and image reconstruction. He is involved in the development of clinical, pre-clinical PET and hadron therapy monitoring scanners. At the time of writing this book he was a lecturer at University of Pisa, teaching courses of life-sciences and medical physics laboratory. He regularly acts as a referee for the following journals: Medical Physics, Physics in Medicine and Biology, Transactions on Medical Imaging, Computers in Biology and Medicine, Physica Medica, EURASIP Journal on Image and Video Processing, Journal of Biomedical and Health Informatics.

 

Author(s): Daniele Panetta, Niccolo Camarlinghi
Series: Focus Series in Medical Physics and Biomedical Engineering
Publisher: CRC Press
Year: 2020

Language: English
Pages: 134
City: Boca Raton

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface
About the Authors
Chapter 1: Preliminary notions
1.1 IMAGE RECONSTRUCTION FROM PROJECTION
1.1.1 Purpose of image reconstruction
1.1.2 Families of reconstruction methods
1.2 TOMOGRAPHIC IMAGING MODALITIES (RELEVANT FOR THIS BOOK)
1.2.1 Computed Tomography (CT)
1.2.2 Positron Emission Tomography (PET)
1.2.3 Single-photon Emission Computed Tomography (SPECT)
1.3 NOTIONS COMMON FOR ALL RECONSTRUCTION METHODS
1.3.1 Object function and image function
1.4 RELEVANT NOTIONS FOR ANALYTICAL RECONSTRUCTION METHODS
1.4.1 Line integral
1.4.2 Radon transform
1.4.3 Sinogram
1.4.4 Exact and approximated reconstruction
1.4.5 Central section theorem
1.5 RELEVANT NOTIONS FOR ITERATIVE RECONSTRUCTION METHODS
1.5.1 Object vector and data vector
1.5.2 System matrix
1.5.3 Discrete forward projection
1.5.4 Discrete back projection
Chapter 2: Short guide to Python samples
2.1 INSTALLATION
2.2 PROJECT ORGANIZATION
2.3 CODING CONVENTIONS
2.4 DEFINITION OF AN EXPERIMENTAL SETUP
2.4.1 Definition of a radiation detector
2.4.2 Definition of the image matrix
2.4.3 PET experimental setup
2.4.4 CT experimental setup
2.4.5 Parallel beam CT
2.4.6 Fan beam CT
2.4.7 Cone beam CT
2.4.8 Serialization/de-serialization of objects
2.4.9 Rendering an experimental setup
2.4.10 3D stack visualization
Chapter 3: Analytical reconstruction algorithms
3.1 2D RECONSTRUCTION IN PARALLEL BEAM GEOMETRY
3.1.1 Direct Fourier Reconstruction (DFR)
3.1.2 Filtered Backprojection (FBP)
3.1.2.1 Filtered Backprojection vs. Convolution Backprojection
3.1.2.2 Ramp filter and apodisation windows
3.1.2.3 The backprojection step
3.1.3 High-level Python implementation of the FBP
3.2 2D FBP IN FAN BEAM GEOMETRY
3.2.1 Rebinning
3.2.2 Full-scan (2p) FBP reconstruction in native fan beam geometry
3.2.3 Python implementation of the fan beam FBP
3.2.4 Data redundancy and short-scan reconstruction
3.3 RECONSTRUCTION OF FAN BEAM DATA FROM HELICAL SCANS
3.4 3D FBP IN CONE BEAM GEOMETRY
3.4.1 The Feldkamp-Davis-Kress (FDK) method
3.4.2 Python implementation of the FDK algorithm
3.5 OTHER FOURIER-BASED METHODS
3.5.1 Backprojection-Filtration (BPF)
3.6 SUGGESTED EXPERIMENTS
Chapter 4: Iterative reconstruction algorithms
4.1 SYSTEM MATRIX
4.2 IMPLEMENTATION OF THE FORWARD AND BACK PROJECTION
4.3 HADAMARD PRODUCT AND DIVISION
4.4 ALGEBRAIC RECONSTRUCTION TECHNIQUE (ART)
4.5 SIMULTANEOUS ITERATIVE RECONSTRUCTION TECHNIQUE (SIRT)
4.6 MAXIMUM-LIKELIHOOD EXPECTATION MAXIMIZATION (MLEM)
4.7 ORDERED-SUBSET EXPECTATION MAXIMIZATION (OSEM)
4.8 A STEP-BY-STEP EXAMPLE USING ARTIFICIAL NOISELESS PROJECTION DATA
4.9 A STEP-BY-STEP EXAMPLE USING ARTIFICIAL POISSON NOISE AFFECTED DATA
4.9.1 Study of convergence properties of the algorithms
4.10 SUGGESTED EXPERIMENTS
Chapter 5: Overview of methods for generation of projection data
5.1 ANALYTICAL PROJECTION OF IDEAL ELLIPSOIDAL PHANTOMS
5.2 NUMERICAL PROJECTION OF VOXELIZED PHANTOMS
5.2.1 Siddon’s Algorithm
Bibliography
Index