Regularized Image Reconstruction In Parallel Mri With Matlab

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 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 (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

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.

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.

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.

This book is a compilation of research work in the interdisciplinary areas of electronics, communication, and computing. This book is specifically targeted at students, research scholars and academicians. The book covers the different approaches and techniques for specific applications, such as particle-swarm optimization, Otsu’s function and harmony search optimization algorithm, triple gate silicon on insulator (SOI)MOSFET, micro-Raman and Fourier Transform Infrared Spectroscopy (FTIR) analysis, high-k dielectric gate oxide, spectrum sensing in cognitive radio, microstrip antenna, Ground-penetrating radar (GPR) with conducting surfaces, and digital image forgery detection. The contents of the book will be useful to academic and professional researchers alike.

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.