Doctor of Philosophy

dissertationDynamic contrast enhanced magnetic resonance imaging (DCE-MRI) is a powerful tool to detect cardiac diseases and tumors, and both spatial resolution and temporal resolution are important for disease detection. Sampling less in each time frame and applying sophisticated reconstruction methods to overcome image degradations is a common strategy in the literature. In this thesis, temporal TV constrained reconstruction that was successfully applied to DCE myocardial perfusion imaging by our group was extended to three-dimensional (3D) DCE breast and 3D myocardial perfusion imaging, and the extension includes different forms of constraint terms and various sampling patterns. We also explored some other popular reconstruction algorithms from a theoretical level and showed that they can be included in a unified framework. Current 3D Cartesian DCE breast tumor imaging is limited in spatiotemporal resolution as high temporal resolution is desired to track the contrast enhancement curves, and high spatial resolution is desired to discern tumor morphology. Here temporal TV constrained reconstruction was extended and different forms of temporal TV constraints were compared on 3D Cartesian DCE breast tumor data with simulated undersampling. Kinetic parameters analysis was used to validate the methods

Inversion of multiconfiguration complex EMI data with minimum gradient support regularization: A case study

Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Their handy size makes these tools very practical for near-surface characterization in many fields of applications, for example, precision agriculture, pollution assessments, and shallow geological investigations. To this end, the inversion of either the real (in-phase) or the imaginary (quadrature) component of the signal has already been studied. Furthermore, in many situations, a regularization scheme retrieving smooth solutions is blindly applied, without taking into account the prior available knowledge. The present work discusses an algorithm for the inversion of the complex signal in its entirety, as well as a regularization method that promotes the sparsity of the reconstructed electrical conductivity distribution. This regularization strategy incorporates a minimum gradient support stabilizer into a truncated generalized singular value decomposition scheme. The results of the implementation of this sparsity-enhancing regularization at each step of a damped Gauss-Newton inversion algorithm (based on a nonlinear forward model) are compared with the solutions obtained via a standard smooth stabilizer. An approach for estimating the depth of investigation, that is, the maximum depth that can be investigated by a chosen instrument configuration in a particular experimental setting is also discussed. The effectiveness and limitations of the whole inversion algorithm are demonstrated on synthetic and real data sets

Visualization and Localization of Interventional Devices with MRI by Susceptibility Mapping

Recently, interventional procedures can be performed with the visual assistance of MRI. However, the devices used in these procedures, such as brachytherapy seeds, biopsy needles, markers, and stents, have a large magnetic susceptibility that leads to severe signal loss and distortion in the MRI images and degrades the accuracy of the localization. Right now, there is no effective way to correctly identify, localize and visualize these interventional devices in MRI images. In this dissertation, we proposed a method to improve the accuracy of localization and visualization by generating positive contrast of the interventional devices using a regularized L1 minimization algorithm. Specifically, the spin-echo sequence with a shifted 180-degree pulse is used to acquire high SNR data. A short shift time is used to avoid severe phase wrap. A phase unwrapping method based on Markov Random Field using Highest-Confidence-First algorithm is proposed to unwrap the phase image. Then the phase images with different shifted time are used to calculate the field map. Next, L1 regularized deconvolution is performed to calculate the susceptibility map. With much higher susceptibility of the interventional devices than the background tissue, the interventional devices show positive-contrast in the susceptibility image. Computer simulations were performed to study the effect of the signal-to-noise ratio, resolution, orientation and size of the interventional devices on the accuracy of the results. Experiments were performed using gelatin and tissue phantom with brachytherapy seeds, gelatin phantoms with platinum wires, and water phantom with titanium needles. The results show that the proposed method provide positive contrast images of these interventional devices, differentiate them from other structures in the MRI images, and improves the visualization and localization of the devices

Efficient Model-Based Reconstruction for Dynamic MRI

Dynamic magnetic resonance imaging (MRI) has important clinical and neuro- science applications (e.g., cardiac disease diagnosis, neurological behavior studies). It captures an object in motion by acquiring data across time, then reconstructing a sequence of images from them. This dissertation considers efficient dynamic MRI reconstruction using handcrafted models, to achieve fast imaging with high spatial and temporal resolution. Our modeling framework considers data acquisition process, image properties, and artifact correction. The reconstruction model expressed as a large-scale inverse problem requires optimization algorithms to solve, and we consider efficient implementations that make use of underlying problem structures. In the context of dynamic MRI reconstruction, we investigate efficient updates in two frameworks of algorithms for solving a nonsmooth composite convex optimization problem for the low-rank plus sparse (L+S) model. In the proximal gradient framework, current algorithms for the L+S model involve the classical iterative soft thresholding algorithm (ISTA); we consider two accelerated alternatives, one based on the fast iterative shrinkage-thresholding algorithm (FISTA), and the other with the recent proximal optimized gradient method (POGM). In the augmented Lagrangian (AL) framework, we propose an efficient variable splitting scheme based on the form of the data acquisition operator, leading to simpler computation than the conjugate gradient (CG) approach required by existing AL methods. Numerical results suggest faster convergence of our efficient implementations in both frameworks, with POGM providing the fastest convergence overall and the practical benefit of being free of algorithm tuning parameters. In the context of magnetic field inhomogeneity correction, we present an efficient algorithm for a regularized field inhomogeneity estimation problem. Most existing minimization techniques are computationally or memory intensive for 3D datasets, and are designed for single-coil MRI. We consider 3D MRI with optional consideration of coil sensitivity and a generalized expression that addresses both multi-echo field map estimation and water-fat imaging. Our efficient algorithm uses a preconditioned nonlinear conjugate gradient method based on an incomplete Cholesky factorization of the Hessian of the cost function, along with a monotonic line search. Numerical experiments show the computational advantage of the proposed algorithm over state- of-the-art methods with similar memory requirements. In the context of task-based functional MRI (fMRI) reconstruction, we introduce a space-time model that represents an fMRI timeseries as a sum of task-correlated signal and non-task background. Our model consists of a spatiotemporal decomposition based on assumptions of the activation waveform shape, with spatial and temporal smoothness regularization on the magnitude and phase of the timeseries. Compared with two contemporary task fMRI decomposition models, our proposed model yields better timeseries and activation maps on simulated and human subject fMRI datasets with multiple tasks. The above examples are part of a larger framework for model-based dynamic MRI reconstruction. This dissertation concludes by presenting a general framework with flexibility on model assumptions and artifact compensation options (e.g., field inhomogeneity, head motion), and proposing future work ideas on both the framework and its connection to data acquisition.PHDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168081/1/yilinlin_1.pd

Fast Magnetic Susceptibility Reconstruction Using L0 Norm Gradient Minimization

在磁共振成像领域，定量磁化率成像技术受到越来越多的关注。磁化率作为组织自身固有的属性，能够提供一种显著的对比度机制和比相位更能反映组织的组成成分。每个组织都有自己的磁化率值，比如含钙和铁沉淀的组织等。到目前为止，磁化率能够为诊断再生障碍性，阿兹海默病，地中海贫血症，血色素沉着症和帕金森症等疾病提供帮助。 定量磁化率成像一般经过三个步骤，第一步是相位解缠绕，第二步是背景场去除，最后是对得到的局部场进行磁化率反演。其中在磁化率反演过程中，由于偶极子核在锥面区域存在零值，使得从局部场到磁化率的反演变成一个病态反问题。在磁化率反演时，噪声和局部场的错误检测都会在这个病态区域得到进一步的扩大。 最近...There is a growing interest in quantifying tissue susceptibility in magnetic resonance imaging. Magnetic susceptibility is an intrinsic tissue property that can be used to provide impressive image contrast and reflects tissue composition much more closely than phase. Different tissues have different magnetic susceptibility, such as calcium and iron-laden tissue and so on. Nowadays, susceptibility ...学位：工学硕士院系专业：信息科学与技术学院_信号与信息处理学号：2332012115299