Compressed sensing recovery with unlearned neural networks

This report investigates methods for solving the problem of compressed sensing, in which the goal is to recover a signal from noisy, linear measurements. Compressed sensing techniques enable signal recovery with far fewer measurements than required by traditional methods such as Nyquist sampling. Signal recovery is an incredibly important area in application domains such as consumer electronics, medical imaging, and many others. While classical methods for compressed sensing recovery are well established, recent developments in machine learning have created wide opportunity for improvement. In this report I first discuss pre-existing approaches, both classical and modern. I then present my own contribution to this field: creating a method using untrained machine learning models. This approach has several advantages which enable its use in complex domains such as medical imagingElectrical and Computer Engineerin

Three-Dimensional Photoacoustic Computed Tomography: Imaging Models and Reconstruction Algorithms

Photoacoustic computed tomography: PACT), also known as optoacoustic tomography, is a rapidly emerging imaging modality that holds great promise for a wide range of biomedical imaging applications. Much effort has been devoted to the investigation of imaging physics and the optimization of experimental designs. Meanwhile, a variety of image reconstruction algorithms have been developed for the purpose of computed tomography. Most of these algorithms assume full knowledge of the acoustic pressure function on a measurement surface that either encloses the object or extends to infinity, which poses many difficulties for practical applications. To overcome these limitations, iterative image reconstruction algorithms have been actively investigated. However, little work has been conducted on imaging models that incorporate the characteristics of data acquisition systems. Moreover, when applying to experimental data, most studies simplify the inherent three-dimensional wave propagation as two-dimensional imaging models by introducing heuristic assumptions on the transducer responses and/or the object structures. One important reason is because three-dimensional image reconstruction is computationally burdensome. The inaccurate imaging models severely limit the performance of iterative image reconstruction algorithms in practice. In the dissertation, we propose a framework to construct imaging models that incorporate the characteristics of ultrasonic transducers. Based on the imaging models, we systematically investigate various iterative image reconstruction algorithms, including advanced algorithms that employ total variation-norm regularization. In order to accelerate three-dimensional image reconstruction, we develop parallel implementations on graphic processing units. In addition, we derive a fast Fourier-transform based analytical image reconstruction formula. By use of iterative image reconstruction algorithms based on the proposed imaging models, PACT imaging scanners can have a compact size while maintaining high spatial resolution. The research demonstrates, for the first time, the feasibility and advantages of iterative image reconstruction algorithms in three-dimensional PACT

Regularisierte Optimierungsverfahren für Rekonstruktion und Modellierung in der Computergraphik

The field of computer graphics deals with virtual representations of the real world. These can be obtained either through reconstruction of a model from measurements, or by directly modeling a virtual object, often on a real-world example. The former is often formalized as a regularized optimization problem, in which a data term ensures consistency between model and data and a regularization term promotes solutions that have high a priori probability. In this dissertation, different reconstruction problems in computer graphics are shown to be instances of a common class of optimization problems which can be solved using a uniform algorithmic framework. Moreover, it is shown that similar optimization methods can also be used to solve data-based modeling problems, where the amount of information that can be obtained from measurements is insufficient for accurate reconstruction. As real-world examples of reconstruction problems, sparsity and group sparsity methods are presented for radio interferometric image reconstruction in static and time-dependent settings. As a modeling example, analogous approaches are investigated to automatically create volumetric models of astronomical nebulae from single images based on symmetry assumptions.Das Feld der Computergraphik beschäftigt sich mit virtuellen Abbildern der realen Welt. Diese können erlangt werden durch Rekonstruktion eines Modells aus Messdaten, oder durch direkte Modellierung eines virtuellen Objekts, oft nach einem realen Vorbild. Ersteres wird oft als regularisiertes Optimierungsproblem dargestellt, in dem ein Datenterm die Konsistenz zwischen Modell und Daten sicherstellt, während ein Regularisierungsterm Lösungen fördert, die eine hohe A-priori-Wahrscheinlichkeit aufweisen. In dieser Arbeit wird gezeigt, dass verschiedene Rekonstruktionsprobleme der Computergraphik Instanzen einer gemeinsamen Klasse von Optimierungsproblemen sind, die mit einem einheitlichen algorithmischen Framework gelöst werden können. Darüber hinaus wird gezeigt, dass vergleichbare Optimierungsverfahren auch genutzt werden können, um Probleme der datenbasierten Modellierung zu lösen, bei denen die aus Messungen verfügbaren Daten nicht für eine genaue Rekonstruktion ausreichen. Als praxisrelevante Beispiele für Rekonstruktionsprobleme werden Sparsity- und Group-Sparsity-Methoden für die radiointerferometrische Bildrekonstruktion im statischen und zeitabhängigen Fall vorgestellt. Als Beispiel für Modellierung werden analoge Verfahren untersucht, um basierend auf Symmetrieannahmen automatisch volumetrische Modelle astronomischer Nebel aus Einzelbildern zu erzeugen

Advancements and Breakthroughs in Ultrasound Imaging

Ultrasonic imaging is a powerful diagnostic tool available to medical practitioners, engineers and researchers today. Due to the relative safety, and the non-invasive nature, ultrasonic imaging has become one of the most rapidly advancing technologies. These rapid advances are directly related to the parallel advancements in electronics, computing, and transducer technology together with sophisticated signal processing techniques. This book focuses on state of the art developments in ultrasonic imaging applications and underlying technologies presented by leading practitioners and researchers from many parts of the world

Microwave Sensing and Imaging

In recent years, microwave sensing and imaging have acquired an ever-growing importance in several applicative fields, such as non-destructive evaluations in industry and civil engineering, subsurface prospection, security, and biomedical imaging. Indeed, microwave techniques allow, in principle, for information to be obtained directly regarding the physical parameters of the inspected targets (dielectric properties, shape, etc.) by using safe electromagnetic radiations and cost-effective systems. Consequently, a great deal of research activity has recently been devoted to the development of efficient/reliable measurement systems, which are effective data processing algorithms that can be used to solve the underlying electromagnetic inverse scattering problem, and efficient forward solvers to model electromagnetic interactions. Within this framework, this Special Issue aims to provide some insights into recent microwave sensing and imaging systems and techniques