Regularized Image Reconstruction In Parallel Mri With Matlab

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Regularized Image Reconstruction in Parallel MRI with MATLAB

Author : Joseph Suresh Paul
Publisher : CRC Press
ISBN 13 : 1351029258
Total Pages : 306 pages
Book Rating : 4.3/5 (51 download)

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Book Synopsis Regularized Image Reconstruction in Parallel MRI with MATLAB by : Joseph Suresh Paul

Download or read book Regularized Image Reconstruction in Parallel MRI with MATLAB written by Joseph Suresh Paul and published by CRC Press. This book was released on 2019-11-05 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Compressed Sensing Magnetic Resonance Image Reconstruction Algorithms

Author : Bhabesh Deka
Publisher : Springer
ISBN 13 : 9811335974
Total Pages : 122 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Compressed Sensing Magnetic Resonance Image Reconstruction Algorithms by : Bhabesh Deka

Download or read book Compressed Sensing Magnetic Resonance Image Reconstruction Algorithms written by Bhabesh Deka and published by Springer. This book was released on 2018-12-29 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive review of the recent developments in fast L1-norm regularization-based compressed sensing (CS) magnetic resonance image reconstruction algorithms. Compressed sensing magnetic resonance imaging (CS-MRI) is able to reduce the scan time of MRI considerably as it is possible to reconstruct MR images from only a few measurements in the k-space; far below the requirements of the Nyquist sampling rate. L1-norm-based regularization problems can be solved efficiently using the state-of-the-art convex optimization techniques, which in general outperform the greedy techniques in terms of quality of reconstructions. Recently, fast convex optimization based reconstruction algorithms have been developed which are also able to achieve the benchmarks for the use of CS-MRI in clinical practice. This book enables graduate students, researchers, and medical practitioners working in the field of medical image processing, particularly in MRI to understand the need for the CS in MRI, and thereby how it could revolutionize the soft tissue imaging to benefit healthcare technology without making major changes in the existing scanner hardware. It would be particularly useful for researchers who have just entered into the exciting field of CS-MRI and would like to quickly go through the developments to date without diving into the detailed mathematical analysis. Finally, it also discusses recent trends and future research directions for implementation of CS-MRI in clinical practice, particularly in Bio- and Neuro-informatics applications.

Compressed Sensing for Engineers

Author : Angshul Majumdar
Publisher : CRC Press
ISBN 13 : 1351261347
Total Pages : 231 pages
Book Rating : 4.3/5 (512 download)

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Book Synopsis Compressed Sensing for Engineers by : Angshul Majumdar

Download or read book Compressed Sensing for Engineers written by Angshul Majumdar and published by CRC Press. This book was released on 2018-12-07 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compressed Sensing (CS) in theory deals with the problem of recovering a sparse signal from an under-determined system of linear equations. The topic is of immense practical significance since all naturally occurring signals can be sparsely represented in some domain. In recent years, CS has helped reduce scan time in Magnetic Resonance Imaging (making scans more feasible for pediatric and geriatric subjects) and has also helped reduce the health hazard in X-Ray Computed CT. This book is a valuable resource suitable for an engineering student in signal processing and requires a basic understanding of signal processing and linear algebra. Covers fundamental concepts of compressed sensing Makes subject matter accessible for engineers of various levels Focuses on algorithms including group-sparsity and row-sparsity, as well as applications to computational imaging, medical imaging, biomedical signal processing, and machine learning Includes MATLAB examples for further development

Image Processing

Author : Artyom M. Grigoryan
Publisher : CRC Press
ISBN 13 : 1351832379
Total Pages : 468 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis Image Processing by : Artyom M. Grigoryan

Download or read book Image Processing written by Artyom M. Grigoryan and published by CRC Press. This book was released on 2018-09-03 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on mathematical methods in computer tomography, Image Processing: Tensor Transform and Discrete Tomography with MATLAB® introduces novel approaches to help in solving the problem of image reconstruction on the Cartesian lattice. Specifically, it discusses methods of image processing along parallel rays to more quickly and accurately reconstruct images from a finite number of projections, thereby avoiding overradiation of the body during a computed tomography (CT) scan. The book presents several new ideas, concepts, and methods, many of which have not been published elsewhere. New concepts include methods of transferring the geometry of rays from the plane to the Cartesian lattice, the point map of projections, the particle and its field function, and the statistical model of averaging. The authors supply numerous examples, MATLAB®-based programs, end-of-chapter problems, and experimental results of implementation. The main approach for image reconstruction proposed by the authors differs from existing methods of back-projection, iterative reconstruction, and Fourier and Radon filtering. In this book, the authors explain how to process each projection by a system of linear equations, or linear convolutions, to calculate the corresponding part of the 2-D tensor or paired transform of the discrete image. They then describe how to calculate the inverse transform to obtain the reconstruction. The proposed models for image reconstruction from projections are simple and result in more accurate reconstructions. Introducing a new theory and methods of image reconstruction, this book provides a solid grounding for those interested in further research and in obtaining new results. It encourages readers to develop effective applications of these methods in CT.

MRI

Author : Angshul Majumdar
Publisher : CRC Press
ISBN 13 : 1482298899
Total Pages : 222 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis MRI by : Angshul Majumdar

Download or read book MRI written by Angshul Majumdar and published by CRC Press. This book was released on 2018-09-03 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of magnetic resonance imaging (MRI) has developed rapidly over the past decade, benefiting greatly from the newly developed framework of compressed sensing and its ability to drastically reduce MRI scan times. MRI: Physics, Image Reconstruction, and Analysis presents the latest research in MRI technology, emphasizing compressed sensing-based image reconstruction techniques. The book begins with a succinct introduction to the principles of MRI and then: Discusses the technology and applications of T1rho MRI Details the recovery of highly sampled functional MRIs Explains sparsity-based techniques for quantitative MRIs Describes multi-coil parallel MRI reconstruction techniques Examines off-line techniques in dynamic MRI reconstruction Explores advances in brain connectivity analysis using diffusion and functional MRIs Featuring chapters authored by field experts, MRI: Physics, Image Reconstruction, and Analysis delivers an authoritative and cutting-edge treatment of MRI reconstruction techniques. The book provides engineers, physicists, and graduate students with a comprehensive look at the state of the art of MRI.

Fundamentals of Magnetic Resonance Imaging with Image Reconstruction Simulated by MATLAB

Author : Jintong Mao
Publisher :
ISBN 13 : 9781710107401
Total Pages : 398 pages
Book Rating : 4.1/5 (74 download)

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Book Synopsis Fundamentals of Magnetic Resonance Imaging with Image Reconstruction Simulated by MATLAB by : Jintong Mao

Download or read book Fundamentals of Magnetic Resonance Imaging with Image Reconstruction Simulated by MATLAB written by Jintong Mao and published by . This book was released on 2019-11-21 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This version of the book is in color printing with a little minor revision.Starting from complex free induction decay (FID), this book establishes a logical framework for the discussion of the principle of MRI. Based on the framework, traditional topics and some new topics are described in detail. Every formula is derived step by step at length. Essence of MRI is thoroughly discussed. It is emphasized that Fourier transform (FT) in MRI is a natural result from data acquisition with linear field gradient. Each concept, particularly the concept of echo, is explained in great detail. For example, it is indicated that the popular drawing of an echo following FID in time axis is misleading in MRI (but not NMR). An echo cannot be considered as two back to back FID, etc. If you cannot accept these statements immediately, you may need to refresh your basic knowledge of MRI. The procedure from FID to MR image is accomplished by a pair of FT. The first FT is established naturally from echo acquisition. Analog digital converter leads to discrete FID. From Nyquist sampling and quadrature phase sensitive detection (PSD), formula FOV*dk = 2pi is derived. From FOV*dk=2pi, discrete FT is derived by the summation of discrete FID directly, without relying on continuous FT. Thus, discrete FID leads to discrete FT. On other side, a discrete echo is the summation of acquired discrete FID, if re-phasing linear gradient field follows de-phasing gradient field. Thus, discrete FID also leads to discrete echo. We have that the discrete echo is a discrete FT (one dimensional). A series of echoes is obtained by phase encoding (raw data in two-dimensional k-space). The k-space is, therefore, a two dimensional discrete FT (first FT). The reconstructed image is obtained by applying inverse FT (second FT) to the series of discrete echoes (k-space). Continuous FT is used as a heuristic step. But it is not necessary for the discussion of MRI. As an example from FID to MR image, simulated images are obtained for graphical phantoms by using MATLAB. In appendix, MATLAB codes for image reconstruction and frequency selective pulses are included. Based on the framework, the topics include basic pulse sequences; pulse train; image contrasts; signal to noise ratio; ringing artifacts; aliasing artifacts; improvement of slice profile of selective pulses (Bloch equation is solved numerically using Runge-Kutta method); fat suppression; magnetization transfer; diffusion; flow image; functional MRI (fMRI for a perceptual alternation is presented), etc. Inside of the framework, emphasized topics include pulsatile ghost artifact for flow, it is simulated by MATLAB and explained by interleaved zero data in k-space; experiments show that traditional explanation of flow mis-registration is not correct; the experiment also shows that the profile of laminar flow looks like a long needle, instead of ellipsoid; Stejskal-Tanner formula for b-value can be obtained by a wrong derivation, thus, the correctness of the formula may be in question; the strength of refocusing gradient for 90d selective pulse is-0.515, instead of commonly used -0.5 (small difference in refocusing strength leads to a large difference in refocusing effects due to non-linearity of Bloch equation); etc. In addition to above topics, Bloch equation with the terms T1, T2, diffusion, flow, etc. is derived by adding independent contributions to dM/dt with a reasonable assumption. It is the hope this book is readable. It is the hope that the journey through the book is a joy, particularly for the first part of the book. This book will be of value to beginners. Perhaps it is valuable to a more extensive readership as well.

Image Processing

Author : Artyom Grigoryan
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (117 download)

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Book Synopsis Image Processing by : Artyom Grigoryan

Download or read book Image Processing written by Artyom Grigoryan and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on mathematical methods in computer tomography, Image Processing: Tensor Transform and Discrete Tomography with MATLAB® introduces novel approaches to help in solving the problem of image reconstruction on the Cartesian lattice. Specifically, it discusses methods of image processing along parallel rays to more quickly and accurately reconstruct images from a finite number of projections, thereby avoiding overradiation of the body during a computed tomography (CT) scan. The book presents several new ideas, concepts, and methods, many of which have not been published elsewhere. New concepts include methods of transferring the geometry of rays from the plane to the Cartesian lattice, the point map of projections, the particle and its field function, and the statistical model of averaging. The authors supply numerous examples, MATLAB®-based programs, end-of-chapter problems, and experimental results of implementation. The main approach for image reconstruction proposed by the authors differs from existing methods of back-projection, iterative reconstruction, and Fourier and Radon filtering. In this book, the authors explain how to process each projection by a system of linear equations, or linear convolutions, to calculate the corresponding part of the 2-D tensor or paired transform of the discrete image. They then describe how to calculate the inverse transform to obtain the reconstruction. The proposed models for image reconstruction from projections are simple and result in more accurate reconstructions. Introducing a new theory and methods of image reconstruction, this book provides a solid grounding for those interested in further research and in obtaining new results. It encourages readers to develop effective applications of these methods in CT.

Proceedings of 3rd International Conference on Computer Vision and Image Processing

Author : Bidyut B. Chaudhuri
Publisher : Springer Nature
ISBN 13 : 9813290889
Total Pages : 472 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Proceedings of 3rd International Conference on Computer Vision and Image Processing by : Bidyut B. Chaudhuri

Download or read book Proceedings of 3rd International Conference on Computer Vision and Image Processing written by Bidyut B. Chaudhuri and published by Springer Nature. This book was released on 2019-10-31 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of carefully selected works presented at the Third International Conference on Computer Vision & Image Processing (CVIP 2018). The conference was organized by the Department of Computer Science and Engineering of PDPM Indian Institute of Information Technology, Design & Manufacturing, Jabalpur, India during September 29–October 01, 2018. All the papers have been rigorously reviewed by the experts from the domain. This 2 volume proceedings include technical contributions in the areas of Image/Video Processing and Analysis; Image/Video Formation and Display; Image/Video Filtering, Restoration, Enhancement and Super-resolution; Image/Video Coding and Transmission; Image/Video Storage, Retrieval and Authentication; Image/Video Quality; Transform-based and Multi-resolution Image/Video Analysis; Biological and Perceptual Models for Image/Video Processing; Machine Learning in Image/Video Analysis; Probability and uncertainty handling for Image/Video Processing; and Motion and Tracking.

Machine Learning for Medical Image Reconstruction

Author : Florian Knoll
Publisher : Springer Nature
ISBN 13 : 3030338436
Total Pages : 274 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Machine Learning for Medical Image Reconstruction by : Florian Knoll

Download or read book Machine Learning for Medical Image Reconstruction written by Florian Knoll and published by Springer Nature. This book was released on 2019-10-24 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Workshop on Machine Learning for Medical Reconstruction, MLMIR 2019, held in conjunction with MICCAI 2019, in Shenzhen, China, in October 2019. The 24 full papers presented were carefully reviewed and selected from 32 submissions. The papers are organized in the following topical sections: deep learning for magnetic resonance imaging; deep learning for computed tomography; and deep learning for general image reconstruction.

Principles of Magnetic Resonance Imaging

Author : Zhi-Pei Liang
Publisher : Wiley-IEEE Press
ISBN 13 :
Total Pages : 442 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Principles of Magnetic Resonance Imaging by : Zhi-Pei Liang

Download or read book Principles of Magnetic Resonance Imaging written by Zhi-Pei Liang and published by Wiley-IEEE Press. This book was released on 2000 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1971 Dr. Paul C. Lauterbur pioneered spatial information encoding principles that made image formation possible by using magnetic resonance signals. Now Lauterbur, "father of the MRI", and Dr. Zhi-Pei Liang have co-authored the first engineering textbook on magnetic resonance imaging. This long-awaited, definitive text will help undergraduate and graduate students of biomedical engineering, biomedical imaging scientists, radiologists, and electrical engineers gain an in-depth understanding of MRI principles. The authors use a signal processing approach to describe the fundamentals of magnetic resonance imaging. You will find a clear and rigorous discussion of these carefully selected essential topics: Mathematical fundamentals Signal generation and detection principles Signal characteristics Signal localization principles Image reconstruction techniques Image contrast mechanisms Image resolution, noise, and artifacts Fast-scan imaging Constrained reconstruction Complete with a comprehensive set of examples and homework problems, Principles of Magnetic Resonance Imaging is the must-read book to improve your knowledge of this revolutionary technique.

Emission Tomography

Author : Miles N. Wernick
Publisher : Elsevier
ISBN 13 : 9780080521879
Total Pages : 596 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Emission Tomography by : Miles N. Wernick

Download or read book Emission Tomography written by Miles N. Wernick and published by Elsevier. This book was released on 2004-12-07 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: PET and SPECT are two of today’s most important medical-imaging methods, providing images that reveal subtle information about physiological processes in humans and animals. Emission Tomography: The Fundamentals of PET and SPECT explains the physics and engineering principles of these important functional-imaging methods. The technology of emission tomography is covered in detail, including historical origins, scientific and mathematical foundations, imaging systems and their components, image reconstruction and analysis, simulation techniques, and clinical and laboratory applications. The book describes the state of the art of emission tomography, including all facets of conventional SPECT and PET, as well as contemporary topics such as iterative image reconstruction, small-animal imaging, and PET/CT systems. This book is intended as a textbook and reference resource for graduate students, researchers, medical physicists, biomedical engineers, and professional engineers and physicists in the medical-imaging industry. Thorough tutorials of fundamental and advanced topics are presented by dozens of the leading researchers in PET and SPECT. SPECT has long been a mainstay of clinical imaging, and PET is now one of the world’s fastest growing medical imaging techniques, owing to its dramatic contributions to cancer imaging and other applications. Emission Tomography: The Fundamentals of PET and SPECT is an essential resource for understanding the technology of SPECT and PET, the most widely used forms of molecular imaging. *Contains thorough tutorial treatments, coupled with coverage of advanced topics *Three of the four holders of the prestigious Institute of Electrical and Electronics Engineers Medical Imaging Scientist Award are chapter contributors *Include color artwork

Practical Image and Video Processing Using MATLAB

Author : Oge Marques
Publisher : John Wiley & Sons
ISBN 13 : 111809347X
Total Pages : 704 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Practical Image and Video Processing Using MATLAB by : Oge Marques

Download or read book Practical Image and Video Processing Using MATLAB written by Oge Marques and published by John Wiley & Sons. This book was released on 2011-08-04 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: UP-TO-DATE, TECHNICALLY ACCURATE COVERAGE OF ESSENTIAL TOPICS IN IMAGE AND VIDEO PROCESSING This is the first book to combine image and video processing with a practical MATLAB®-oriented approach in order to demonstrate the most important image and video techniques and algorithms. Utilizing minimal math, the contents are presented in a clear, objective manner, emphasizing and encouraging experimentation. The book has been organized into two parts. Part I: Image Processing begins with an overview of the field, then introduces the fundamental concepts, notation, and terminology associated with image representation and basic image processing operations. Next, it discusses MATLAB® and its Image Processing Toolbox with the start of a series of chapters with hands-on activities and step-by-step tutorials. These chapters cover image acquisition and digitization; arithmetic, logic, and geometric operations; point-based, histogram-based, and neighborhood-based image enhancement techniques; the Fourier Transform and relevant frequency-domain image filtering techniques; image restoration; mathematical morphology; edge detection techniques; image segmentation; image compression and coding; and feature extraction and representation. Part II: Video Processing presents the main concepts and terminology associated with analog video signals and systems, as well as digital video formats and standards. It then describes the technically involved problem of standards conversion, discusses motion estimation and compensation techniques, shows how video sequences can be filtered, and concludes with an example of a solution to object detection and tracking in video sequences using MATLAB®. Extra features of this book include: More than 30 MATLAB® tutorials, which consist of step-by-step guides toexploring image and video processing techniques using MATLAB® Chapters supported by figures, examples, illustrative problems, and exercises Useful websites and an extensive list of bibliographical references This accessible text is ideal for upper-level undergraduate and graduate students in digital image and video processing courses, as well as for engineers, researchers, software developers, practitioners, and anyone who wishes to learn about these increasingly popular topics on their own.

Deblurring Images

Author : Per Christian Hansen
Publisher : SIAM
ISBN 13 : 9780898718874
Total Pages : 144 pages
Book Rating : 4.7/5 (188 download)

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Book Synopsis Deblurring Images by : Per Christian Hansen

Download or read book Deblurring Images written by Per Christian Hansen and published by SIAM. This book was released on 2006-01-01 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the deblurring algorithms and techniques collectively known as spectral filtering methods, in which the singular value decomposition, or a similar decomposition with spectral properties, is used to introduce the necessary regularization or filtering in the reconstructed image. The concise MATLAB® implementations described in the book provide a template of techniques that can be used to restore blurred images from many applications.

Anisotropic Diffusion in Image Processing

Author : J. Weickert
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis Anisotropic Diffusion in Image Processing by : J. Weickert

Download or read book Anisotropic Diffusion in Image Processing written by J. Weickert and published by . This book was released on 1996 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of MRI Pulse Sequences

Author : Matt A. Bernstein
Publisher : Elsevier
ISBN 13 : 0080533124
Total Pages : 1041 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of MRI Pulse Sequences by : Matt A. Bernstein

Download or read book Handbook of MRI Pulse Sequences written by Matt A. Bernstein and published by Elsevier. This book was released on 2004-09-21 with total page 1041 pages. Available in PDF, EPUB and Kindle. Book excerpt: Magnetic Resonance Imaging (MRI) is among the most important medical imaging techniques available today. There is an installed base of approximately 15,000 MRI scanners worldwide. Each of these scanners is capable of running many different "pulse sequences", which are governed by physics and engineering principles, and implemented by software programs that control the MRI hardware. To utilize an MRI scanner to the fullest extent, a conceptual understanding of its pulse sequences is crucial. Handbook of MRI Pulse Sequences offers a complete guide that can help the scientists, engineers, clinicians, and technologists in the field of MRI understand and better employ their scanner. Explains pulse sequences, their components, and the associated image reconstruction methods commonly used in MRI Provides self-contained sections for individual techniques Can be used as a quick reference guide or as a resource for deeper study Includes both non-mathematical and mathematical descriptions Contains numerous figures, tables, references, and worked example problems

Handbook of Mathematical Methods in Imaging

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
ISBN 13 : 0387929193
Total Pages : 1626 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Handbook of Mathematical Methods in Imaging by : Otmar Scherzer

Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Introduction to Functional Analysis

Author : Christian Clason
Publisher : Springer Nature
ISBN 13 : 3030527840
Total Pages : 166 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Introduction to Functional Analysis by : Christian Clason

Download or read book Introduction to Functional Analysis written by Christian Clason and published by Springer Nature. This book was released on 2020-11-30 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis has become one of the essential foundations of modern applied mathematics in the last decades, from the theory and numerical solution of differential equations, from optimization and probability theory to medical imaging and mathematical image processing. This textbook offers a compact introduction to the theory and is designed to be used during one semester, fitting exactly 26 lectures of 90 minutes each. It ranges from the topological fundamentals recalled from basic lectures on real analysis to spectral theory in Hilbert spaces. Special attention is given to the central results on dual spaces and weak convergence.