Inverse Problem Formulation and Deep Learning Methods for Ultrasound Beamforming and Image Reconstruction

Ultrasound imaging is among the most common medical imaging modalities, which has the advantages of being real-time, non-invasive, cost-effective, and portable. Medical ultrasound images, however, have low values of signal-to-noise ratio due to many factors, and there has been a long-standing line of research on improving the quality of ultrasound images. Ultrasound transducers are made from piezoelectric elements, which are responsible for the insonification of the medium with non-invasive acoustic waves and also the reception of backscattered signals. Design optimizations span all steps of the image formation pipeline, including system architecture, hardware development, and software algorithms. Each step entails parameter optimizations and trade-offs in order to achieve a balance in competing effects such as cost, performance, and efficiency. The current thesis is devoted to research on image reconstruction techniques in order to push forward the classical limitations. It is tried not to be restricted into a specific class of computational imaging or machine learning method. As such, classical approaches and recent methods based on deep learning are adapted according to the requirements and limitations of the image reconstruction problem. In other words, we aim to reconstruct a high-quality spatial map of the medium echogenicity from raw channel data received from piezoelectric elements. All other steps of the ultrasound image formation pipeline are considered fixed, and the goal is to extract the best possible image quality (in terms of resolution, contrast, speckle pattern, etc.) from echo traces acquired by transducer elements. Two novel approaches are proposed on super-resolution ultrasound imaging by training deep models that create mapping functions from observations recorded from a single transmission to high-quality images. These models are mainly developed to resolve the necessity of several transmissions, which can potentially be used in applications that require both high framerate and image quality. The remaining four contributions are on beamforming, which is an essential step in medical ultrasound image reconstruction. Different approaches, including independent component analysis, deep learning, and inverse problem formulations, are utilized to tackle the ill-posed inverse problem of receive beamforming. The primary goal of novel beamformers is to find a solution to the trade-off between image quality and framerate. The final chapter consists of concluding remarks on each of our contributions, where the strengths and weaknesses of our proposed techniques based on classical computational imaging and deep learning methods are outlined. There is still a large room for improvement in all of our proposed techniques, and the thesis is concluded by providing avenues for future research to attain those improvements

Deep Learning in Medical Image Analysis

The accelerating power of deep learning in diagnosing diseases will empower physicians and speed up decision making in clinical environments. Applications of modern medical instruments and digitalization of medical care have generated enormous amounts of medical images in recent years. In this big data arena, new deep learning methods and computational models for efficient data processing, analysis, and modeling of the generated data are crucially important for clinical applications and understanding the underlying biological process. This book presents and highlights novel algorithms, architectures, techniques, and applications of deep learning for medical image analysis

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal