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3D Image Reconstruction for CT and PET: A Practical Guide with Python [Kõva köide]

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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 andcompact 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 imagereconstruction. 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"--

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.

 

Preface xi
About the Authors xv
Chapter 1 Preliminary notions
1(16)
1.1 Image Reconstruction From Projection
1(3)
1.1.1 Purpose Of Image Reconstruction
1(1)
1.1.2 Families Of Reconstruction Methods
2(2)
1.2 Tomographic Imaging Modalities (Relevant For This Book)
4(3)
1.2.1 Computed Tomography (Ct)
4(1)
1.2.2 Positron Emission Tomography (Pet)
4(2)
1.2.3 Single-Photon Emission Computed Tomography (Spect)
6(1)
1.3 Notions Common For All Reconstruction Methods
7(1)
1.3.1 Object Function And Image Function
7(1)
1.4 Relevant Notions For Analytical Reconstruction Methods
8(3)
1.4.1 Line Integral
8(1)
1.4.2 Radon Transform
8(1)
1.4.3 Sinogram
9(1)
1.4.4 Exact and approximated reconstruction
9(1)
1.4.5 Central section theorem
10(1)
1.5 Relevant Notions For Iterative Reconstruction Methods
11(6)
1.5.1 Object vector and data vector
11(1)
1.5.2 System matrix
12(2)
1.5.3 Discrete forward projection
14(1)
1.5.4 Discrete back projection
14(3)
Chapter 2 Short guide to Python samples
17(10)
2.1 Installation
17(1)
2.2 Project Organization
17(1)
2.3 Coding Conventions
18(1)
2.4 Definition Of An Experimental Setup
18(9)
2.4.1 Definition of a radiation detector
19(1)
2.4.2 Definition of the image matrix
20(1)
2.4.3 PET experimental setup
21(1)
2.4.4 CT experimental setup
21(1)
2.4.5 Parallel beam CT
21(1)
2.4.6 Fan beam CT
22(1)
2.4.7 Cone beam CT
22(2)
2.4.8 Serialization/de-serialization of objects
24(1)
2.4.9 Rendering an experimental setup
24(1)
2.4.10 3D stack visualization
25(2)
Chapter 3 Analytical reconstruction algorithms
27(56)
3.1 2D Reconstruction In Parallel Beam Geometry
29(22)
3.1.1 Direct Fourier Reconstruction (DFR)
29(7)
3.1.2 Filtered Backprojection (FBP)
36(2)
3.1.2.1 Filtered Backprojection vs. Convolution Backprojection
38(1)
3.1.2.2 Ramp filter and apodisation windows
38(6)
3.1.2.3 The backprojection step
44(5)
3.1.3 High-level Python implementation of the FBP
49(2)
3.2 2D FBP In Fan Beam Geometry
51(14)
3.2.1 Rebinning
51(2)
3.2.2 Full-scan (27r) FBP reconstruction in native fan beam geometry
53(4)
3.2.3 Python implementation of the fan beam FBP
57(5)
3.2.4 Data redundancy and short-scan reconstruction
62(3)
3.3 Reconstruction Of Fan Beam Data From Helical Scans
65(3)
3.4 3D FBP In Cone Beam Geometry
68(10)
3.4.1 The Feldkamp-Davis-Kress (FDK) method
69(5)
3.4.2 Python implementation of the FDK algorithm
74(4)
3.5 Other Fourier-Based Methods
78(4)
3.5.1 Backprojection-Filtration (BPF)
78(4)
3.6 Suggested Experiments
82(1)
Chapter 4 Iterative Reconstruction Algorithms
83(22)
4.1 System Matrix
85(1)
4.2 Implementation Of The Forward And Back Projection
86(1)
4.3 Hadamard Product And Division
86(1)
4.4 Algebraic Reconstruction Technique (Art)
87(2)
4.5 Simultaneous Iterative Reconstruction Technique (Sirt)
89(1)
4.6 Maximum-Likelihood Expectation Maximization (Mlem)
90(2)
4.7 Ordered-Subset Expectation Maximization (Osem)
92(2)
4.8 A Step-By-Step Example Using Artificial Noiseless Projection Data
94(5)
4.9 A Step-By-Step Example Using Artificial Poisson Noise Affected Data
99(5)
4.9.1 Study Of Convergence Properties Of The Algorithms
99(5)
4.10 Suggested Experiments
104(1)
Chapter 5 Overview Of Methods For Generation Of Projection Data
105(6)
5.1 Analytical Projection Of Ideal Ellipsoidal Phantoms
105(3)
5.2 Numerical Projection Of Voxelized Phantoms
108(3)
5.2.1 Siddon's Algorithm
108(3)
Bibliography 111(6)
Index 117
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.