3d Image Reconstruction For Ct And Pet

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.

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.

The application of 3D methodology has recently been receiving increasing attention at many PET centres, and this monograph is an attempt to provide a state-of-the-art review of this methodology, covering 3D reconstruction methods, quantitative procedures, current tomography performance, and clinical and research applications. No such review has been available until now to assist PET researchers in understanding and implementing 3D methodology, and in evaluating the performance of the available imaging technology. In all the chapters, the subject matter is treated in sufficient depth to appeal equally to the physicist or engineer who wishes to establish the methodology, and to PET investigators with experience in 2D PET who wish to familiarize themselves with the concepts and advantages of 3D, and to be made aware of the pitfalls.

This book contains a selection of communications presented at the Third International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, held 4-6 July 1995 at Domaine d' Aix-Marlioz, Aix-Ies-Bains, France. This nice resort provided an inspiring environment to hold discussions and presentations on new and developing issues. Roentgen discovered X-ray radiation in 1895 and Becquerel found natural radioactivity in 1896 : a hundred years later, this conference was focused on the applications of such radiations to explore the human body. If the physics is now fully understood, 3D imaging techniques based on ionising radiations are still progressing. These techniques include 3D Radiology, 3D X-ray Computed Tomography (3D-CT), Single Photon Emission Computed Tomography (SPECT), Positron Emission Tomography (PET). Radiology is dedicated to morphological imaging, using transmitted radiations from an external X-ray source, and nuclear medicine to functional imaging, using radiations emitted from an internal radioactive tracer. In both cases, new 3D tomographic systems will tend to use 2D detectors in order to improve the radiation detection efficiency. Taking a set of 2D acquisitions around the patient, 3D acquisitions are obtained. Then, fully 3D image reconstruction algorithms are required to recover the 3D image of the body from these projection measurements.

"Medical Image Reconstruction: A Conceptual Tutorial" introduces the classical and modern image reconstruction technologies, such as two-dimensional (2D) parallel-beam and fan-beam imaging, three-dimensional (3D) parallel ray, parallel plane, and cone-beam imaging. This book presents both analytical and iterative methods of these technologies and their applications in X-ray CT (computed tomography), SPECT (single photon emission computed tomography), PET (positron emission tomography), and MRI (magnetic resonance imaging). Contemporary research results in exact region-of-interest (ROI) reconstruction with truncated projections, Katsevich's cone-beam filtered backprojection algorithm, and reconstruction with highly undersampled data with l0-minimization are also included. This book is written for engineers and researchers in the field of biomedical engineering specializing in medical imaging and image processing with image reconstruction. Gengsheng Lawrence Zeng is an expert in the development of medical image reconstruction algorithms and is a professor at the Department of Radiology, University of Utah, Salt Lake City, Utah, USA.

This book introduces the classical and modern image reconstruction technologies. It covers topics in two-dimensional (2D) parallel-beam and fan-beam imaging, three-dimensional (3D) parallel ray, parallel plane, and cone-beam imaging. Both analytical and iterative methods are presented. The applications in X-ray CT, SPECT (single photon emission computed tomography), PET (positron emission tomography), and MRI (magnetic resonance imaging) are discussed. Contemporary research results in exact region-of-interest (ROI) reconstruction with truncated projections, Katsevich’s cone-beam filtered backprojection algorithm, and reconstruction with highly under-sampled data are included. The last chapter of the book is devoted to the techniques of using a fast analytical algorithm to reconstruct an image that is equivalent to an iterative reconstruction. These techniques are the author’s most recent research results. This book is intended for students, engineers, and researchers who are interested in medical image reconstruction. Written in a non-mathematical way, this book provides an easy access to modern mathematical methods in medical imaging. Table of Content: Chapter 1 Basic Principles of Tomography 1.1 Tomography 1.2 Projection 1.3 Image Reconstruction 1.4 Backprojection 1.5 Mathematical Expressions Problems References Chapter 2 Parallel-Beam Image Reconstruction 2.1 Fourier Transform 2.2 Central Slice Theorem 2.3 Reconstruction Algorithms 2.4 A Computer Simulation 2.5 ROI Reconstruction with Truncated Projections 2.6 Mathematical Expressions (The Fourier Transform and Convolution , The Hilbert Transform and the Finite Hilbert Transform , Proof of the Central Slice Theorem, Derivation of the Filtered Backprojection Algorithm , Expression of the Convolution Backprojection Algorithm, Expression of the Radon Inversion Formula ,Derivation of the Backprojection-then-Filtering Algorithm Problems References Chapter 3 Fan-Beam Image Reconstruction 3.1 Fan-Beam Geometry and Point Spread Function 3.2 Parallel-Beam to Fan-Beam Algorithm Conversion 3.3 Short Scan 3.4 Mathematical Expressions (Derivation of a Filtered Backprojection Fan-Beam Algorithm, A Fan-Beam Algorithm Using the Derivative and the Hilbert Transform) Problems References Chapter 4 Transmission and Emission Tomography 4.1 X-Ray Computed Tomography 4.2 Positron Emission Tomography and Single Photon Emission Computed Tomography 4.3 Attenuation Correction for Emission Tomography 4.4 Mathematical Expressions Problems References Chapter 5 3D Image Reconstruction 5.1 Parallel Line-Integral Data 5.2 Parallel Plane-Integral Data 5.3 Cone-Beam Data (Feldkamp's Algorithm, Grangeat's Algorithm, Katsevich's Algorithm) 5.4 Mathematical Expressions (Backprojection-then-Filtering for Parallel Line-Integral Data, Filtered Backprojection Algorithm for Parallel Line-Integral Data, 3D Radon Inversion Formula, 3D Backprojection-then-Filtering Algorithm for Radon Data, Feldkamp's Algorithm, Tuy's Relationship, Grangeat's Relationship, Katsevich’s Algorithm) Problems References Chapter 6 Iterative Reconstruction 6.1 Solving a System of Linear Equations 6.2 Algebraic Reconstruction Technique 6.3 Gradient Descent Algorithms 6.4 Maximum-Likelihood Expectation-Maximization Algorithms 6.5 Ordered-Subset Expectation-Maximization Algorithm 6.6 Noise Handling (Analytical Methods, Iterative Methods, Iterative Methods) 6.7 Noise Modeling as a Likelihood Function 6.8 Including Prior Knowledge 6.9 Mathematical Expressions (ART, Conjugate Gradient Algorithm, ML-EM, OS-EM, Green’s One-Step Late Algorithm, Matched and Unmatched Projector/Backprojector Pairs ) 6.10 Reconstruction Using Highly Undersampled Data with l0 Minimization Problems References Chapter 7 MRI Reconstruction 7.1 The 'M' 7.2 The 'R' 7.3 The 'I'; (To Obtain z-Information, x-Information, y-Information) 7.4 Mathematical Expressions Problems References Indexing

This book constitutes the refereed joint proceedings of the International Workshop on Computational Methods for Molecular Imaging, CMMI 2017, the International Workshop on Reconstruction and Analysis of Moving Body Organs, RAMBO 2017, and the International Stroke Workshop: Imaging and Treatment Challenges, SWITCH 2017, held in conjunction with the 20th International Conference on Medical Imaging and Computer-Assisted Intervention, MICCAI 2017, in Québec City, QC, Canada, in September 2017. The 5 full papers presented at FIFI 2017, the 9 full papers presented at RAMBO 2017, and the 4 full papers presented at SWITCH 2017 were carefully reviewed and selected. The CMMI papers cover various areas from image synthesis to data analysis and from clinical diagnosis to therapy individualization, using molecular imaging modalities PET, SPECT, PET/CT, SPECT/CT, and PET/MR. The RAMBO papers present research from both academia and industry, They are organized into the categories "registration and tracking" and "image reconstruction and information retrieval" while application areas include cardiac, pulmonal, abdominal, fetal, and renal imaging. The SWITCH papers focus on CT(A)-based quantitative imaging biomarkers for stroke.

It gives me immense pleasure to introduce this timely handbook to the research/- velopment communities in the ?eld of signal processing systems (SPS). This is the ?rst of its kind and represents state-of-the-arts coverage of research in this ?eld. The driving force behind information technologies (IT) hinges critically upon the major advances in both component integration and system integration. The major breakthrough for the former is undoubtedly the invention of IC in the 50’s by Jack S. Kilby, the Nobel Prize Laureate in Physics 2000. In an integrated circuit, all components were made of the same semiconductor material. Beginning with the pocket calculator in 1964, there have been many increasingly complex applications followed. In fact, processing gates and memory storage on a chip have since then grown at an exponential rate, following Moore’s Law. (Moore himself admitted that Moore’s Law had turned out to be more accurate, longer lasting and deeper in impact than he ever imagined. ) With greater device integration, various signal processing systems have been realized for many killer IT applications. Further breakthroughs in computer sciences and Internet technologies have also catalyzed large-scale system integration. All these have led to today’s IT revolution which has profound impacts on our lifestyle and overall prospect of humanity. (It is hard to imagine life today without mobiles or Internets!) The success of SPS requires a well-concerted integrated approach from mul- ple disciplines, such as device, design, and application.