Acceleration Methods for MRI

Acceleration methods are a critical area of research for MRI. Two of the most important acceleration techniques involve parallel imaging and compressed sensing. These advanced signal processing techniques have the potential to drastically reduce scan times and provide radiologists with new information for diagnosing disease. However, many of these new techniques require solving difficult optimization problems, which motivates the development of more advanced algorithms to solve them. In addition, acceleration methods have not reached maturity in some applications, which motivates the development of new models tailored to these applications. This dissertation makes advances in three different areas of accelerations. The first is the development of a new algorithm (called B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithm or BARISTA), that solves a parallel MRI optimization problem with compressed sensing assumptions. BARISTA is shown to be 2-3 times faster and more robust to parameter selection than current state-of-the-art variable splitting methods. The second contribution is the extension of BARISTA ideas to non-Cartesian trajectories that also leads to a 2-3 times acceleration over previous methods. The third contribution is the development of a new model for functional MRI that enables a 3-4 factor of acceleration of effective temporal resolution in functional MRI scans. Several variations of the new model are proposed, with an ROC curve analysis showing that a combination low-rank/sparsity model giving the best performance in identifying the resting-state motor network.PhDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120841/1/mmuckley_1.pd

On the Relationship between Conjugate Gradient and Optimal First-Order Methods for Convex Optimization

In a series of work initiated by Nemirovsky and Yudin, and later extended by Nesterov, first-order algorithms for unconstrained minimization with optimal theoretical complexity bound have been proposed. On the other hand, conjugate gradient algorithms as one of the widely used first-order techniques suffer from the lack of a finite complexity bound. In fact their performance can possibly be quite poor. This dissertation is partially on tightening the gap between these two classes of algorithms, namely the traditional conjugate gradient methods and optimal first-order techniques. We derive conditions under which conjugate gradient methods attain the same complexity bound as in Nemirovsky-Yudin's and Nesterov's methods. Moreover, we propose a conjugate gradient-type algorithm named CGSO, for Conjugate Gradient with Subspace Optimization, achieving the optimal complexity bound with the payoff of a little extra computational cost. We extend the theory of CGSO to convex problems with linear constraints. In particular we focus on solving $l_1$-regularized least square problem, often referred to as Basis Pursuit Denoising (BPDN) problem in the optimization community. BPDN arises in many practical fields including sparse signal recovery, machine learning, and statistics. Solving BPDN is fairly challenging because the size of the involved signals can be quite large; therefore first order methods are of particular interest for these problems. We propose a quasi-Newton proximal method for solving BPDN. Our numerical results suggest that our technique is computationally effective, and can compete favourably with the other state-of-the-art solvers

Text Similarity Between Concepts Extracted from Source Code and Documentation

Context: Constant evolution in software systems often results in its documentation losing sync with the content of the source code. The traceability research field has often helped in the past with the aim to recover links between code and documentation, when the two fell out of sync. Objective: The aim of this paper is to compare the concepts contained within the source code of a system with those extracted from its documentation, in order to detect how similar these two sets are. If vastly different, the difference between the two sets might indicate a considerable ageing of the documentation, and a need to update it. Methods: In this paper we reduce the source code of 50 software systems to a set of key terms, each containing the concepts of one of the systems sampled. At the same time, we reduce the documentation of each system to another set of key terms. We then use four different approaches for set comparison to detect how the sets are similar. Results: Using the well known Jaccard index as the benchmark for the comparisons, we have discovered that the cosine distance has excellent comparative powers, and depending on the pre-training of the machine learning model. In particular, the SpaCy and the FastText embeddings offer up to 80% and 90% similarity scores. Conclusion: For most of the sampled systems, the source code and the documentation tend to contain very similar concepts. Given the accuracy for one pre-trained model (e.g., FastText), it becomes also evident that a few systems show a measurable drift between the concepts contained in the documentation and in the source code.</p