Image Reconstruction
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| Author | : Mehmet Akcakaya |
| Publisher | : Academic Press |
| Total Pages | : 518 |
| Release | : 2022-11-04 |
| Genre | : Science |
| ISBN | : 012822746X |
Magnetic Resonance Image Reconstruction: Theory, Methods and Applications presents the fundamental concepts of MR image reconstruction, including its formulation as an inverse problem, as well as the most common models and optimization methods for reconstructing MR images. The book discusses approaches for specific applications such as non-Cartesian imaging, under sampled reconstruction, motion correction, dynamic imaging and quantitative MRI. This unique resource is suitable for physicists, engineers, technologists and clinicians with an interest in medical image reconstruction and MRI. Explains the underlying principles of MRI reconstruction, along with the latest research“/li> Gives example codes for some of the methods presented Includes updates on the latest developments, including compressed sensing, tensor-based reconstruction and machine learning based reconstruction
| Author | : Gengsheng Lawrence Zeng |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 289 |
| Release | : 2017-03-20 |
| Genre | : Medical |
| ISBN | : 3110498022 |
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
| Author | : Gengsheng Zeng |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 204 |
| Release | : 2010-12-28 |
| Genre | : Technology & Engineering |
| ISBN | : 3642053688 |
"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.
| Author | : Gabor T. Herman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 302 |
| Release | : 2009-07-14 |
| Genre | : Computers |
| ISBN | : 1846287235 |
This revised and updated second edition – now with two new chapters - is the only book to give a comprehensive overview of computer algorithms for image reconstruction. It covers the fundamentals of computerized tomography, including all the computational and mathematical procedures underlying data collection, image reconstruction and image display. Among the new topics covered are: spiral CT, fully 3D positron emission tomography, the linogram mode of backprojection, and state of the art 3D imaging results. It also includes two new chapters on comparative statistical evaluation of the 2D reconstruction algorithms and alternative approaches to image reconstruction.
| Author | : A.P. Korostelev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 272 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461227127 |
There exists a large variety of image reconstruction methods proposed by different authors (see e. g. Pratt (1978), Rosenfeld and Kak (1982), Marr (1982)). Selection of an appropriate method for a specific problem in image analysis has been always considered as an art. How to find the image reconstruction method which is optimal in some sense? In this book we give an answer to this question using the asymptotic minimax approach in the spirit of Ibragimov and Khasminskii (1980a,b, 1981, 1982), Bretagnolle and Huber (1979), Stone (1980, 1982). We assume that the image belongs to a certain functional class and we find the image estimators that achieve the best order of accuracy for the worst images in the class. This concept of optimality is rather rough since only the order of accuracy is optimized. However, it is useful for comparing various image reconstruction methods. For example, we show that some popular methods such as simple linewise processing and linear estimation are not optimal for images with sharp edges. Note that discontinuity of images is an important specific feature appearing in most practical situations where one has to distinguish between the "image domain" and the "background" . The approach of this book is based on generalization of nonparametric regression and nonparametric change-point techniques. We discuss these two basic problems in Chapter 1. Chapter 2 is devoted to minimax lower bounds for arbitrary estimators in general statistical models.
| Author | : Frank Natterer |
| Publisher | : SIAM |
| Total Pages | : 226 |
| Release | : 2001-01-01 |
| Genre | : Computers |
| ISBN | : 0898716225 |
This book provides readers with a superior understanding of the mathematical principles behind imaging.
| Author | : Vivek Bannore |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 121 |
| Release | : 2009-04-08 |
| Genre | : Mathematics |
| ISBN | : 3642003842 |
To my wife, Mitu - Vivek Bannore Preface Preface In many imaging systems, under-sampling and aliasing occurs frequently leading to degradation of image quality. Due to the limited number of sensors available on the digital cameras, the quality of images captured is also limited. Factors such as optical or atmospheric blur and sensor noise can also contribute further to the d- radation of image quality. Super-Resolution is an image reconstruction technique that enhances a sequence of low-resolution images or video frames by increasing the spatial resolution of the images. Each of these low-resolution images contain only incomplete scene information and are geometrically warped, aliased, and - der-sampled. Super-resolution technique intelligently fuses the incomplete scene information from several consecutive low-resolution frames to reconstruct a hi- resolution representation of the original scene. In the last decade, with the advent of new technologies in both civil and mi- tary domain, more computer vision applications are being developed with a demand for high-quality high-resolution images. In fact, the demand for high- resolution images is exponentially increasing and the camera manufacturing te- nology is unable to cope up due to cost efficiency and other practical reasons.
| Author | : Stephen Maybank |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 268 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642775578 |
The image taken by a moving camera changes with time. These image motions contain information about the motion of the camera and about the shapes of the objects in the field of view. There are two main types of image motion, finite displacements and image velocities. Finite displacements are described by the point correspondences between two images of the same scene taken from different positions. Image velocities are the velocities of the points in the image as they move over the projection surface. Reconstruction is the task of obtaining from the image-motions information about the camera motion or about the shapes of objects in the field of view. In this book the theory underlying reconstruction is described. Reconstruction from image motion is the subject matter of two different sci entific disciplines, photogrammetry and computer vision. In photogrammetry the accuracy of reconstruction is emphasised; in computer vision the emphasis is on methods for obtaining information from images in real time in order to guide a mechanical device such as a robot arm or an automatic vehicle. This book arises from recent work carried out in computer vision. Computer vision is a young field but it is developing rapidly. The earliest papers on reconstruction in the computer vision literature date back only to the mid 1970s. As computer vision develops, the mathematical techniques applied to the analysis of recon struction become more appropriate and more powerful.
| Author | : Joseph Suresh Paul |
| Publisher | : CRC Press |
| Total Pages | : 306 |
| Release | : 2019-11-05 |
| Genre | : Medical |
| ISBN | : 1351029258 |
Regularization becomes an integral part of the reconstruction process in accelerated parallel magnetic resonance imaging (pMRI) due to the need for utilizing the most discriminative information in the form of parsimonious models to generate high quality images with reduced noise and artifacts. Apart from providing a detailed overview and implementation details of various pMRI reconstruction methods, Regularized image reconstruction in parallel MRI with MATLAB examples interprets regularized image reconstruction in pMRI as a means to effectively control the balance between two specific types of error signals to either improve the accuracy in estimation of missing samples, or speed up the estimation process. The first type corresponds to the modeling error between acquired and their estimated values. The second type arises due to the perturbation of k-space values in autocalibration methods or sparse approximation in the compressed sensing based reconstruction model. Features: Provides details for optimizing regularization parameters in each type of reconstruction. Presents comparison of regularization approaches for each type of pMRI reconstruction. Includes discussion of case studies using clinically acquired data. MATLAB codes are provided for each reconstruction type. Contains method-wise description of adapting regularization to optimize speed and accuracy. This book serves as a reference material for researchers and students involved in development of pMRI reconstruction methods. Industry practitioners concerned with how to apply regularization in pMRI reconstruction will find this book most useful.
| Author | : Jong Chul Ye |
| Publisher | : Cambridge University Press |
| Total Pages | : 365 |
| Release | : 2023-09-30 |
| Genre | : Technology & Engineering |
| ISBN | : 1316517519 |
Discover the power of deep neural networks for image reconstruction with this state-of-the-art review of modern theories and applications. The background theory of deep learning is introduced step-by-step, and by incorporating modeling fundamentals this book explains how to implement deep learning in a variety of modalities, including X-ray, CT, MRI and others. Real-world examples demonstrate an interdisciplinary approach to medical image reconstruction processes, featuring numerous imaging applications. Recent clinical studies and innovative research activity in generative models and mathematical theory will inspire the reader towards new frontiers. This book is ideal for graduate students in Electrical or Biomedical Engineering or Medical Physics.
