Handbook of Mathematical Methods in Imaging

Handbook of Mathematical Methods in Imaging
Author: Otmar Scherzer
Publisher: Springer Science & Business Media
Total Pages: 1626
Release: 2010-11-23
Genre: Mathematics
ISBN: 0387929193

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.

Regularized Image Reconstruction in Parallel MRI with MATLAB

Regularized Image Reconstruction in Parallel MRI with MATLAB
Author: Joseph Suresh Paul
Publisher: CRC Press
Total Pages: 289
Release: 2019-11-05
Genre: Medical
ISBN: 135102924X

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.

Theoretical Foundations and Numerical Methods for Sparse Recovery

Theoretical Foundations and Numerical Methods for Sparse Recovery
Author: Massimo Fornasier
Publisher: Walter de Gruyter
Total Pages: 351
Release: 2010-07-30
Genre: Mathematics
ISBN: 3110226154

The present collection is the very first contribution of this type in the field of sparse recovery. Compressed sensing is one of the important facets of the broader concept presented in the book, which by now has made connections with other branches such as mathematical imaging, inverse problems, numerical analysis and simulation. The book consists of four lecture notes of courses given at the Summer School on "Theoretical Foundations and Numerical Methods for Sparse Recovery" held at the Johann Radon Institute for Computational and Applied Mathematics in Linz, Austria, in September 2009. This unique collection will be of value for a broad community and may serve as a textbook for graduate courses. From the contents: "Compressive Sensing and Structured Random Matrices" by Holger Rauhut "Numerical Methods for Sparse Recovery" by Massimo Fornasier "Sparse Recovery in Inverse Problems" by Ronny Ramlau and Gerd Teschke "An Introduction to Total Variation for Image Analysis" by Antonin Chambolle, Vicent Caselles, Daniel Cremers, Matteo Novaga and Thomas Pock

Computational Methods for Inverse Problems

Computational Methods for Inverse Problems
Author: Curtis R. Vogel
Publisher: SIAM
Total Pages: 195
Release: 2002-01-01
Genre: Mathematics
ISBN: 0898717574

Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Image Processing Based on Partial Differential Equations

Image Processing Based on Partial Differential Equations
Author: Xue-Cheng Tai
Publisher: Springer Science & Business Media
Total Pages: 440
Release: 2006-11-22
Genre: Computers
ISBN: 3540332677

This book publishes a collection of original scientific research articles that address the state-of-art in using partial differential equations for image and signal processing. Coverage includes: level set methods for image segmentation and construction, denoising techniques, digital image inpainting, image dejittering, image registration, and fast numerical algorithms for solving these problems.

Level Set and PDE Based Reconstruction Methods in Imaging

Level Set and PDE Based Reconstruction Methods in Imaging
Author: Martin Burger
Publisher: Springer
Total Pages: 329
Release: 2013-10-17
Genre: Mathematics
ISBN: 3319017128

This book takes readers on a tour through modern methods in image analysis and reconstruction based on level set and PDE techniques, the major focus being on morphological and geometric structures in images. The aspects covered include edge-sharpening image reconstruction and denoising, segmentation and shape analysis in images, and image matching. For each, the lecture notes provide insights into the basic analysis of modern variational and PDE-based techniques, as well as computational aspects and applications.

ICAOS ’96 12th International Conference on Analysis and Optimization of Systems

ICAOS ’96 12th International Conference on Analysis and Optimization of Systems
Author: Marie-Odile Berger
Publisher: Springer
Total Pages: 386
Release: 1996-06-25
Genre: Computers
ISBN:

This volume contains the proceedings of ICAOS '96 the 12th International Conference on Analysis and Optimization of Systems. This conference was co-organized by INRIA and the CEREMADE and was dedicated to Images, Wavelets and PDE's. The aim of the conference was to discuss the impact on image analysis of recent mathematical developments in multiscale analysis, partial differential equations, variational methods and so on. ICAOS '96 provided a forum for image processing researchers and mathematicians to interact and to exchange their technical knowledge and experience, theoretical or practical, in this emerging and exciting domain. The selected papers have been organized according to the following sessions, each session corresponding to a section of the book: 1. Active Contours; 2. Image Enhancement and Restoration, Scale-Spaces; 3. Wavelets; 4. Image Segmentation; 5. Image Restoration; 6. Coding; 7. Applications.

Variational Methods in Imaging

Variational Methods in Imaging
Author: Otmar Scherzer
Publisher: Springer Science & Business Media
Total Pages: 323
Release: 2008-09-26
Genre: Mathematics
ISBN: 0387692770

This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.

Mathematical Methods in Engineering

Mathematical Methods in Engineering
Author: Nuno Miguel Fonseca Ferreira
Publisher: Springer
Total Pages: 311
Release: 2014-08-18
Genre: Technology & Engineering
ISBN: 9400771835

This book presents a careful selection of the contributions presented at the Mathematical Methods in Engineering (MME10) International Symposium, held at the Polytechnic Institute of Coimbra- Engineering Institute of Coimbra (IPC/ISEC), Portugal, October 21-24, 2010. The volume discusses recent developments about theoretical and applied mathematics toward the solution of engineering problems, thus covering a wide range of topics, such as: Automatic Control, Autonomous Systems, Computer Science, Dynamical Systems and Control, Electronics, Finance and Economics, Fluid Mechanics and Heat Transfer, Fractional Mathematics, Fractional Transforms and Their Applications, Fuzzy Sets and Systems, Image and Signal Analysis, Image Processing, Mechanics, Mechatronics, Motor Control and Human Movement Analysis, Nonlinear Dynamics, Partial Differential Equations, Robotics, Acoustics, Vibration and Control, and Wavelets.