Toeplitz-Based Iterative Image Reconstruction for MRI With Correction for Magnetic Field Inhomogeneity

In some types of magnetic resonance (MR) imaging, particularly functional brain scans, the conventional Fourier model for the measurements is inaccurate. Magnetic field inhomogeneities, which are caused by imperfect main fields and by magnetic susceptibility variations, induce distortions in images that are reconstructed by conventional Fourier methods. These artifacts hamper the use of functional MR imaging (fMRI) in brain regions near air/tissue interfaces. Recently, iterative methods that combine the conjugate gradient (CG) algorithm with nonuniform FFT (NUFFT) operations have been shown to provide considerably improved image quality relative to the conjugate-phase method. However, for non-Cartesian k-space trajectories, each CG-NUFFT iteration requires numerous k-space interpolations; these are operations that are computationally expensive and poorly suited to fast hardware implementations. This paper proposes a faster iterative approach to field-corrected MR image reconstruction based on the CG algorithm and certain Toeplitz matrices. This CG-Toeplitz approach requires k-space interpolations only for the initial iteration; thereafter, only fast Fourier transforms (FFTs) are required. Simulation results show that the proposed CG-Toeplitz approach produces equivalent image quality as the CG-NUFFT method with significantly reduced computation time.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85903/1/Fessler50.pd

Improved 3D MR Image Acquisition and Processing in Congenital Heart Disease

Congenital heart disease (CHD) is the most common type of birth defect, affecting about 1% of the population. MRI is an essential tool in the assessment of CHD, including diagnosis, intervention planning and follow-up. Three-dimensional MRI can provide particularly rich visualization and information. However, it is often complicated by long scan times, cardiorespiratory motion, injection of contrast agents, and complex and time-consuming postprocessing. This thesis comprises four pieces of work that attempt to respond to some of these challenges. The first piece of work aims to enable fast acquisition of 3D time-resolved cardiac imaging during free breathing. Rapid imaging was achieved using an efficient spiral sequence and a sparse parallel imaging reconstruction. The feasibility of this approach was demonstrated on a population of 10 patients with CHD, and areas of improvement were identified. The second piece of work is an integrated software tool designed to simplify and accelerate the development of machine learning (ML) applications in MRI research. It also exploits the strengths of recently developed ML libraries for efficient MR image reconstruction and processing. The third piece of work aims to reduce contrast dose in contrast-enhanced MR angiography (MRA). This would reduce risks and costs associated with contrast agents. A deep learning-based contrast enhancement technique was developed and shown to improve image quality in real low-dose MRA in a population of 40 children and adults with CHD. The fourth and final piece of work aims to simplify the creation of computational models for hemodynamic assessment of the great arteries. A deep learning technique for 3D segmentation of the aorta and the pulmonary arteries was developed and shown to enable accurate calculation of clinically relevant biomarkers in a population of 10 patients with CHD

Advanced image reconstruction in parallel magnetic resonance imaging : constraints and solutions.

Thesis (Ph. D.)--Harvard-MIT Division of Health Sciences and Technology, 2005.Includes bibliographical references.Imaging speed is a crucial consideration for magnetic resonance imaging (MRI). The speed of conventional MRI is limited by hardware performance and physiological safety measures. "Parallel" MRI is a new technique that circumvents these limitations by utilizing arrays of radiofrequency detector coils to acquire data in parallel, thereby enabling still higher imaging speeds. In parallel MRI, coil arrays are used to accomplish part of the spatial encoding that was traditionally performed by magnetic field gradients alone. MR signal data acquired with coil arrays are spatially encoded with the distinct reception patterns of the individual coil elements. T[he quality of parallel MR images is dictated by the accuracy and efficiency of an image reconstruction (decoding) strategy. This thesis formulates the spatial encoding and decoding of parallel MRI as a generalized linear inverse problem. Under this linear algebraic framework, theoretical and empirical limits on the performance of parallel MR image reconstructions are characterized, and solutions are proposed to facilitate routine clinical and research applications. Each research study presented in this thesis addresses one or more elements in the inverse problem, and the studies are collectively arranged to reflect three progressive stages in solving the inverse problem: 1) determining the encoding matrix, 2) computing a matrix inverse, 3) characterizing the error involved. First, a self-calibrating strategy is proposed which uses non-Cartesian trajectories to automatically determine coil sensitivities without the need of an external scan or modification of data acquisition, guaranteeing an accurate formulation of the encoding matrix.(cont.) Second, two matrix inversion strategies are presented which, respectively, exploit physical properties of coil encoding and the phase information of the magnetization. While the former allows stable and distributable matrix inversion using the k-space locality principle, the latter integrates parallel image reconstruction with conjugate symmetry. Third, a numerical strategy is presented for computing noise statistics of parallel MRI techniques which involve magnitude image combination, enabling quantitative image comparison. In addition, fundamental limits on the performance of parallel image reconstruction are derived using the Cramer-Rao bounds. Lastly, the practical applications of techniques developed in this thesis are demonstrated by a case study in improved coronary angiography.Ph.D

Optimal spectral reconstructions from deterministic and stochastic sampling geometries using compressive sensing and spectral statistical models

This dissertation focuses on the development of high-quality image reconstruction methods from a limited number of Fourier samples using optimized, stochastic and deterministic sampling geometries. Two methodologies are developed: an optimal image reconstruction framework based on Compressive Sensing (CS) techniques and a new, Spectral Statistical approach based on the use of isotropic models over a dyadic partitioning of the spectrum. The proposed methods are demonstrated in applications in reconstructing fMRI and remote sensing imagery. Typically, a reduction in MRI image acquisition time is achieved by sampling K-space at a rate below the Nyquist rate. Various methods using correlation between samples, sample averaging, and more recently, Compressive Sensing, are employed to mitigate the aliasing effects of under-sampled Fourier data. The proposed solution utilizes an additional layer of optimization to enhance the performance of a previously published CS reconstruction algorithm. Specifically, the new framework provides reconstructions of a desired image quality by jointly optimizing for the optimal K-space sampling geometry and CS model parameters. The effectiveness of each geometry is evaluated based on the required number of FFT samples that are available for image reconstructions of sufficient quality. A central result of this approach is that the fastest geometry, the spiral low-pass geometry has also provided the best (optimized) CS reconstructions. This geometry provided significantly better reconstructions than the stochastic sampling geometries recommended in the literature. An optimization framework for selecting appropriate CS model reconstruction parameters is also provided. Here, the term appropriate CS parameters\u27 is meant to infer that the estimated parameter ranges can provide some guarantee for a minimum level of image reconstruction performance. Utilizing the simplex search algorithm, the optimal TV-norm and Wavelet transform penalties are calculated for the CS reconstruction objective function. Collecting the functional evaluation values of the simplex search over a large data set allows for a range of objective function weighting parameters to be defined for the sampling geometries that were found to be effective. The results indicate that the CS parameter optimization framework is significant in that it can provide for large improvements over the standard use of non-optimized approaches. The dissertation also develops the use of a new Spectral Statistical approach for spectral reconstruction of remote sensing imagery. The motivation for pursuing this research includes potential applications that include, but are not limited to, the development of better image compression schemas based on a limited number of spectral coefficients. In addition, other applications include the use of spectral interpolation methods for remote sensing systems that directly sample the Fourier domain optically or electromagnetically, which may suffer from missing or degraded samples beyond and/or within the focal plane. For these applications, a new spectral statistical methodology is proposed that reconstructs spectral data from uniformly spaced samples over a dyadic partition of the spectrum. Unlike the CS approach that solves for the 2D FFT coefficients directly, the statistical approach uses separate models for the magnitude and phase, allowing for separate control of the reconstruction quality of each one. A scalable solution that partitions the spectral domain into blocks of varying size allows for the determination of the appropriate covariance models of the magnitude and phase spectra bounded by the blocks. The individual spectral models are then applied to solving for the optimal linear estimate, which is referred to in literature as Kriging. The use of spectral data transformations are also presented as a means for producing data that is better suited for statistical modeling and variogram estimation. A logarithmic transformation is applied to the magnitude spectra, as it has been shown to impart intrinsic stationarity over localized, bounded regions of the spectra. Phase spectra resulting from the 2D FFT can be best described as being uniformly distributed over the interval of -pi to pi. In this original state, the spectral samples fail to produce appropriate spectral statistical models that exhibit inter-sample covariance. For phase spectra modeling, an unwrapping step is required to ensure that individual blocks can be effectively modeled using appropriate variogram models. The transformed magnitude and unwrapped phase spectra result in unique statistical models that are optimal over individual frequency blocks, which produce accurate spectral reconstructions that account for localized variability in the spectral domain. The Kriging spectral estimates are shown to produce higher quality magnitude and phase spectra reconstructions than the cubic spline, nearest neighbor, and bilinear interpolators that are widely used. Even when model assumptions, such as isotropy, violate the spectral data being modeled, excellent reconstructions are still obtained. Finally, both of the spectral estimation methods developed in this dissertation are compared against one another, revealing how each one of the methods developed here is appropriate for different classes of images. For satellite images that contain a large amount of detail, the new spectral statistical approach, reconstructing the spectrum much faster, from a fraction of the original high frequency content, provided significantly better reconstructions than the best reconstructions from the optimized CS geometries. This result is supported not only by comparing image quality metrics, but also by visual assessment.\u2

Advances in Quantitative MRI: Acquisition, Estimation, and Application

Quantitative magnetic resonance imaging (QMRI) produces images of potential MR biomarkers: measurable tissue properties related to physiological processes that characterize the onset and progression of specific disorders. Though QMRI has potential to be more diagnostic than conventional qualitative MRI, QMRI poses challenges beyond those of conventional MRI that limit its feasibility for routine clinical use. This thesis first seeks to address two of those challenges. It then applies these solutions to develop a new method for myelin water imaging, a challenging application that may be specifically indicative of certain white matter (WM) disorders. One challenge that presently precludes widespread clinical adoption of QMRI involves long scan durations: to disentangle potential biomarkers from nuisance MR contrast mechanisms, QMRI typically requires more data than conventional MRI and thus longer scans. Even allowing for long scans, it has previously been unclear how to systematically tune the "knobs" of MR acquisitions to reliably enable precise biomarker estimation. Chapter 4 formalizes these challenges as a min-max optimal acquisition design problem and solves this problem to design three fast steady-state (SS) acquisitions for precise T1/T2 estimation, a popular QMRI application. The resulting optimized acquisition designs illustrate that acquisition design can enable new biomarker estimation techniques from established MR pulse sequences, a fact that subsequent chapters exploit. Another QMRI challenge involves the typically nonlinear dependence of MR signal models on the underlying biomarkers: these nonlinearities cause conventional likelihood-based estimators to either scale very poorly with the number of unknowns or risk producing suboptimal estimates due to spurious local minima. Chapter 5 instead introduces a fast, general method for dictionary-free QMRI parameter estimation via regression with kernels (PERK). PERK first uses prior distributions and the nonlinear MR signal model to simulate many parameter-measurement pairs. Inspired by machine learning, PERK then takes these pairs as labeled training points and learns from them a nonlinear regression function using kernel functions and convex optimization. Chapter 5 demonstrates PERK for T1/T2 estimation using one of the acquisitions optimized in Chapter 4. Simulations as well as single-slice phantom and in vivo experiments demonstrated that PERK and two well-suited maximum-likelihood (ML) estimators produce comparable T1/T2 estimates, but PERK is consistently at least 140x faster. Similar comparisons to an ML estimator in a more challenging problem (Chapter 6) suggest that this 140x acceleration factor will increase by several orders of magnitude for full-volume QMRI estimation problems involving more latent parameters per voxel. Chapter 6 applies ideas developed in previous chapters to design a new fast method for imaging myelin water content, a potential biomarker for healthy myelin. It first develops a two-compartment dual-echo steady-state (DESS) signal model and then uses a Bayesian variation of acquisition design (Chapter 4) to optimize a new DESS acquisition for precise myelin water imaging. The precision-optimized acquisition is as fast as conventional SS myelin water imaging acquisitions, but enables 2-3x better expected coefficients of variation in fast-relaxing fraction estimates. Simulations demonstrate that PERK (Chapter 5) and ML fast-relaxing fraction estimates from the proposed DESS acquisition exhibit comparable root mean-squared errors, but PERK is more than 500x faster. In vivo experiments are to our knowledge the first to demonstrate lateral WM myelin water content estimates from a fast (3m15s) SS acquisition that are similar to conventional estimates from a slower (32m4s) MESE acquisition.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147486/1/gnataraj_1.pd

Innovative Concepts for the Electronic Interface of Massively Parallel MRI Phased Imaging Arrays

In Magnetic Resonance Imaging (MRI), the concept of parallel imaging shows significant enhancements in boosting the signal-to-noise ratio, reducing the imaging time, and enlarging the imaging field of view. However, this concept necessitates increased size, cost, and complexity of the MR system. This thesis introduces an innovative solution for the electronics of the MRI system that allows parallel imaging with massive number of channels while avoiding, at the same time, the associated drawback