Level Set And Pde Based Reconstruction Methods In Imaging

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.

Here is, for the first time, a book that clearly explains and applies new level set methods to problems and applications in computer vision, graphics, and imaging. It is an essential compilation of survey chapters from the leading researchers in the field. The applications of the methods are emphasized.

This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.

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.

This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning. No other framework can provide comparable accuracy and precision to imaging and vision. Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services. This work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists.

Based on the most novel approaches and cutting-edge clinical and scientific information regarding radionuclide imaging and therapies for neuroendocrine tumors, this clinical guidebook represents a unique collaborative effort between endocrinologists, nuclear physicians, oncologists, surgeons, physicists, radio-pharmacists and geneticists. It begins with the embryology, classification and molecular genetics of gastroenteropancreatic neuroendocrine tumors and carcinoids, chromaffin cell tumors, and MEN1- and MEN2-related tumors. Following a chapter on radiopharmaceuticals in neuroendocrine imaging, it turns to the physics and technology of current and cutting-edge radiology, including SPECT/CT and PET/CT and PET/MR. Discussing of radionuclide imaging covers the tumors mentioned above, as well as pulmonary and thymic neuroendocrine tumors and medullary thyroid carcinoma. A presentation of radionuclide therapies follows, including 131I-MIBG therapy, somatostatin receptor-based therapy, and alpha radionuclide therapy, as well as the role of nanoparticles. Comprehensive and up-to-date, Diagnostic and Therapeutic Nuclear Medicine for Neuroendocrine Tumors will assist and guide physicians who encounter patients with these conditions, either from a diagnostic or therapeutic standpoint, and particularly emphasizes the current and emerging medical devices and imaging and therapeutic options.

Level set methods are numerical techniques which offer remarkably powerful tools for understanding, analyzing, and computing interface motion in a host of settings. When used for medical imaging analysis and segmentation, the function assigns a label to each pixel or voxel and optimality is defined based on desired imaging properties. This often includes a detection step to extract specific objects via segmentation. This allows for the segmentation and analysis problem to be formulated and solved in a principled way based on well-established mathematical theories. Level set method is a great tool for modeling time varying medical images and enhancement of numerical computations.

"Beyond Wavelets" presents state-of-the-art theories, methods, algorithms, and applications of mathematical extensions for classical wavelet analysis. Wavelets, introduced 20 years ago byMorlet and Grossmann and developed very rapidly during the 1980's and 1990's, has created a common link between computational mathematics and other disciplines of science and engineering.Classical wavelets have provided effective and efficient mathematical tools for time-frequency analysis which enhances and replaces the Fourier approach.However, with the current advances in science and technology, there is an immediate need to extend wavelet mathematical tools as well. "Beyond Wavelets" presents a list of ideas and mathematicalfoundations for such extensions, including: continuous and digital ridgelets, brushlets, steerable wavelet packets, contourlets, eno-wavelets, spline-wavelet frames, and quasi-affine wavelets. Wavelet subband algorithms are extended to pyramidal directional and nonuniform filter banks. In addition, this volume includes amethod for tomographic reconstruction using a mechanical image model and a statistical study for independent adaptive signal representation.Investigators already familiar with wavelet methods from areas such as engineering, statistics, and mathematics will benefit by owning this volume. *Curvelets, Contourlets, Ridgelets, *Digital Implementation of Ridgelet Packets*Steerable Wavelet Packets*Essentially Non-Oscillatory Wavelets*Medical Imaging*Non-Uniform Filter Banks*Spline-wavelet frames and *Vanishing Moment Recovery Functions