Methods for Improving MRI-Based Conductivity Mapping

The electrical properties - permittivity and conductivity - of a material describe how electromagnetic waves behave in that material. Electrical properties are frequency-dependent parameters and, for a liquid sample, are measured with a dielectric probe and a network analyzer. This measurement technique is not feasible in vivo, but methods have been developed to make these measurements using magnetic resonance imaging (MRI). This work focuses on measuring conductivity, or the ability to conduct electric current. Mapping the electrical properties within the human body can provide important information for MRI safety and diagnostic applications. First, the specific absorption rate (SAR) in an MRI scan is proportional to conductivity, and limited to minimize the risk of heating in a subject. Knowledge of subject-specific conductivity maps could lead to better, subject-specific SAR estimation. Second, several small studies in recent years have shown that conductivity is elevated in malignant tumors as compared to healthy tissue. There are open research questions regarding the correlation between conductivity and other diagnostic metrics. Both of these applications benefit from accurate conductivity maps. In this work we describe three different methods for improving the accuracy of conductivity maps. The first is a novel regularized, model-based approach which we refer to as the Inverse Laplacian method. The Inverse Laplacian method resulted in lower reconstruction bias and error due to noise in simulations than the conventional filtering method. The Inverse Laplacian method also produced conductivity maps closer to the measured values in a phantom and with reduced noise in the human brain, as compared to the filtering method. The second is a method for combining multi-coil MRI data for conductivity mapping, because the use of multi-coil receivers can drastically improve the SNR in conductivity maps. The noise in the combined phase data using the proposed method was slightly elevated as compared to the optimal combination method, but the conductivity uniformity in a uniform gel phantom was greater than that of the optimal combination method. Furthermore, by visual inspection, the human brain conductivity calculated from data combined using the proposed method had minimal bias and noise amplification. Finally, we present a method for mapping conductivity tensors, as opposed to scalar values, which provides an additional layer of information to conductivity maps. Our proposed mathematical framework yields accurate tensor quantities provided the object can rotate 90 degrees in any direction. However, restricting the object rotation to mimic the constraints on a human subject yields slightly inaccurate results. We also present a dictionary-based approach to tensor calculations to try to improve the tensor estimates using restricted rotations.PHDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144027/1/kropella_1.pd

Generative Adversarial Networks in Computer Vision: A Survey and Taxonomy

Generative adversarial networks (GANs) have been extensively studied in the past few years. Arguably their most significant impact has been in the area of computer vision where great advances have been made in challenges such as plausible image generation, image-to-image translation, facial attribute manipulation and similar domains. Despite the significant successes achieved to date, applying GANs to real-world problems still poses significant challenges, three of which we focus on here. These are: (1) the generation of high quality images, (2) diversity of image generation, and (3) stable training. Focusing on the degree to which popular GAN technologies have made progress against these challenges, we provide a detailed review of the state of the art in GAN-related research in the published scientific literature. We further structure this review through a convenient taxonomy we have adopted based on variations in GAN architectures and loss functions. While several reviews for GANs have been presented to date, none have considered the status of this field based on their progress towards addressing practical challenges relevant to computer vision. Accordingly, we review and critically discuss the most popular architecture-variant, and loss-variant GANs, for tackling these challenges. Our objective is to provide an overview as well as a critical analysis of the status of GAN research in terms of relevant progress towards important computer vision application requirements. As we do this we also discuss the most compelling applications in computer vision in which GANs have demonstrated considerable success along with some suggestions for future research directions. Code related to GAN-variants studied in this work is summarized on https://github.com/sheqi/GAN_Review.Comment: Accepted by ACM Computing Surveys, 23 November 202

Sparse Predictive Modeling : A Cost-Effective Perspective

Many real life problems encountered in industry, economics or engineering are complex and difficult to model by conventional mathematical methods. Machine learning provides a wide variety of methods and tools for solving such problems by learning mathematical models from data. Methods from the field have found their way to applications such as medical diagnosis, financial forecasting, and web-search engines. The predictions made by a learned model are based on a vector of feature values describing the input to the model. However, predictions do not come for free in real world applications, since the feature values of the input have to be bought, measured or produced before the model can be used. Feature selection is a process of eliminating irrelevant and redundant features from the model. Traditionally, it has been applied for achieving interpretable and more accurate models, while the possibility of lowering prediction costs has received much less attention in the literature. In this thesis we consider novel feature selection techniques for reducing prediction costs. The contributions of this thesis are as follows. First, we propose several cost types characterizing the cost of performing prediction with a trained model. Particularly, we consider costs emerging from multitarget prediction problems as well as a number of cost types arising when the feature extraction process is structured. Second, we develop greedy regularized least-squares methods to maximize the predictive performance of the models under given budget constraints. Empirical evaluations are performed on numerous benchmark data sets as well as on a novel water quality analysis application. The results demonstrate that in settings where the considered cost types apply, the proposed methods lead to substantial cost savings compared to conventional methods

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Learning with Low-Quality Data: Multi-View Semi-Supervised Learning with Missing Views

The focus of this thesis is on learning approaches for what we call ``low-quality data'' and in particular data in which only small amounts of labeled target data is available. The first part provides background discussion on low-quality data issues, followed by preliminary study in this area. The remainder of the thesis focuses on a particular scenario: multi-view semi-supervised learning. Multi-view learning generally refers to the case of learning with data that has multiple natural views, or sets of features, associated with it. Multi-view semi-supervised learning methods try to exploit the combination of multiple views along with large amounts of unlabeled data in order to learn better predictive functions when limited labeled data is available. However, lack of complete view data limits the applicability of multi-view semi-supervised learning to real world data. Commonly, one data view is readily and cheaply available, but additionally views may be costly or only available in some cases. This thesis work aims to make multi-view semi-supervised learning approaches more applicable to real world data specifically by addressing the issue of missing views through both feature generation and active learning, and addressing the issue of model selection for semi-supervised learning with limited labeled data. This thesis introduces a unified approach for handling missing view data in multi-view semi-supervised learning tasks, which applies to both data with completely missing additional views and data only missing views in some instances. The idea is to learn a feature generation function mapping one view to another with the mapping biased to encourage the features generated to be useful for multi-view semi-supervised learning algorithms. The mapping is then used to fill in views as pre-processing. Unlike previously proposed single-view multi-view learning approaches, the proposed approach is able to take advantage of additional view data when available, and for the case of partial view presence is the first feature-generation approach specifically designed to take into account the multi-view semi-supervised learning aspect. The next component of this thesis is the analysis of an active view completion scenario. In some tasks, it is possible to obtain missing view data for a particular instance, but with some associated cost. Recent work has shown an active selection strategy can be more effective than a random one. In this thesis, a better understanding of active approaches is sought, and it is demonstrated that the effectiveness of an active selection strategy over a random one can depend on the relationship between the views. Finally, an important component of making multi-view semi-supervised learning applicable to real world data is the task of model selection, an open problem which is often avoided entirely in previous work. For cases of very limited labeled training data the commonly used cross-validation approach can become ineffective. This thesis introduces a re-training alternative to the method-dependent approaches similar in motivation to cross-validation, that involves generating new training and test data by sampling from the large amount of unlabeled data and estimated conditional probabilities for the labels. The proposed approaches are evaluated on a variety of multi-view semi-supervised learning data sets, and the experimental results demonstrate their efficacy

Space adaptive and hierarchical Bayesian variational models for image restoration

The main contribution of this thesis is the proposal of novel space-variant regularization or penalty terms motivated by a strong statistical rational. In light of the connection between the classical variational framework and the Bayesian formulation, we will focus on the design of highly flexible priors characterized by a large number of unknown parameters. The latter will be automatically estimated by setting up a hierarchical modeling framework, i.e. introducing informative or non-informative hyperpriors depending on the information at hand on the parameters. More specifically, in the first part of the thesis we will focus on the restoration of natural images, by introducing highly parametrized distribution to model the local behavior of the gradients in the image. The resulting regularizers hold the potential to adapt to the local smoothness, directionality and sparsity in the data. The estimation of the unknown parameters will be addressed by means of non-informative hyperpriors, namely uniform distributions over the parameter domain, thus leading to the classical Maximum Likelihood approach. In the second part of the thesis, we will address the problem of designing suitable penalty terms for the recovery of sparse signals. The space-variance in the proposed penalties, corresponding to a family of informative hyperpriors, namely generalized gamma hyperpriors, will follow directly from the assumption of the independence of the components in the signal. The study of the properties of the resulting energy functionals will thus lead to the introduction of two hybrid algorithms, aimed at combining the strong sparsity promotion characterizing non-convex penalty terms with the desirable guarantees of convex optimization