Direction Finding in Partly Calibrated Arrays Exploiting the Whole Array Aperture

We consider the problem of direction finding using partly calibrated arrays, a distributed subarray with position errors between subarrays. The key challenge is to enhance angular resolution in the presence of position errors. To achieve this goal, existing algorithms, such as subspace separation and sparse recovery, have to rely on multiple snapshots, which increases the burden of data transmission and the processing delay. Therefore, we aim to enhance angular resolution using only a single snapshot. To this end, we exploit the orthogonality of the signals of partly calibrated arrays. Particularly, we transform the signal model into a special multiple-measurement model, show that there is approximate orthogonality between the source signals in this model, and then use blind source separation to exploit the orthogonality. Simulation and experiment results both verify that our proposed algorithm achieves high angular resolution as distributed arrays without position errors, inversely proportional to the whole array aperture

Compact Formulations for Sparse Reconstruction in Fully and Partly Calibrated Sensor Arrays

Sensor array processing is a classical field of signal processing which offers various applications in practice, such as direction of arrival estimation or signal reconstruction, as well as a rich theory, including numerous estimation methods and statistical bounds on the achievable estimation performance. A comparably new field in signal processing is given by sparse signal reconstruction (SSR), which has attracted remarkable interest in the research community during the last years and similarly offers plentiful fields of application. This thesis considers the application of SSR in fully calibrated sensor arrays as well as in partly calibrated sensor arrays. The main contributions are a novel SSR method for application in partly calibrated arrays as well as compact formulations for the SSR problem, where special emphasis is given on exploiting specific structure in the signals as well as in the array topologies

Multi-frequency image reconstruction for radio-interferometry with self-tuned regularization parameters

As the world's largest radio telescope, the Square Kilometer Array (SKA) will provide radio interferometric data with unprecedented detail. Image reconstruction algorithms for radio interferometry are challenged to scale well with TeraByte image sizes never seen before. In this work, we investigate one such 3D image reconstruction algorithm known as MUFFIN (MUlti-Frequency image reconstruction For radio INterferometry). In particular, we focus on the challenging task of automatically finding the optimal regularization parameter values. In practice, finding the regularization parameters using classical grid search is computationally intensive and nontrivial due to the lack of ground- truth. We adopt a greedy strategy where, at each iteration, the optimal parameters are found by minimizing the predicted Stein unbiased risk estimate (PSURE). The proposed self-tuned version of MUFFIN involves parallel and computationally efficient steps, and scales well with large- scale data. Finally, numerical results on a 3D image are presented to showcase the performance of the proposed approach

Radio measurements for determining the energy scale of cosmic rays

This work is about Tunka-Rex, a radio detector for air showers in Siberia. After calibrating the detector and developing a reconstruction method for air shower events, three results are presented, obtained from the 2012-2014 data of Tunka-Rex: - a method for measuring the energy with a single antenna station. - a validation of the CoREAS code for simulation of radio emission. - a comparison of dofferent experiments\u27s energy scales via the radio signal

CALIBRATION OF AN ULTRASONIC TRANSMISSIVE COMPUTED TOMOGRAPHY SYSTEM

Tato dizertace je zaměřena na medicínskou zobrazovací modalitu – ultrazvukovou počítačovou tomografii – a algoritmy zlepšující kvalitu zobrazení, zejména kalibraci USCT přístroje. USCT je novou modalitou kombinující ultrazvukový přenos signálů a principy tomografické rekonstrukce obrazů vyvíjených pro jiné tomografické systémy. V principu lze vytvořit kvantitativní 3D obrazové objemy s vysokým rozlišením a kontrastem. USCT je primárně určeno pro diagnózu rakoviny prsu. Autor spolupracoval na projektu Institutu Zpracování dat a Elektroniky, Forschungszentrum Karlsruhe, kde je USCT systém vyvíjen. Jeden ze zásadních problémů prototypu USCT v Karlsruhe byla absence kalibrace. Tisíce ultrazvukových měničů se liší v citlivosti, směrovosti a frekvenční odezvě. Tyto parametry jsou navíc proměnné v čase. Další a mnohem závažnější problém byl v pozičních odchylkách jednotlivých měničů. Všechny tyto aspekty mají vliv na konečnou kvalitu rekonstruovaných obrazů. Problém kalibrace si autor zvolil jako hlavní téma dizertace. Tato dizertace popisuje nové metody v oblastech rekonstrukce útlumových obrazů, kalibrace citlivosti měničů a zejména geometrická kalibrace pozic měničů. Tyto metody byly implementovány a otestovány na reálných datech pocházejících z prototypu USCT z Karlsruhe.This dissertation is centered on a medical imaging modality – the ultrasonic computed tomography (USCT) – and algorithms which improve the resulting image quality, namely the calibration of a USCT device. The USCT is a novel imaging modality which combines the phenomenon of ultrasound and image reconstruction principles developed for other tomographic systems. It is capable of producing quantitative 3D image volumes with high resolution and tissue contrast and is primarily aimed at breast cancer diagnosis. The author was involved in a joint research project at the Institute of Data Processing and Electronics, Forschungszentrum Karlsruhe (German National Research Center), where a USCT system is being developed. One of the main problems in the Karlsruhe USCT prototype was the absence of any calibration. The thousands of transducers used in the system have deviations in sensitivity, directivity, and frequency response. These parameters change over time as the transducers age. Also the mechanical positioning of the transducer elements is not precise. All these aspects greatly affect the overall quality of the reconstructed images. The problem of calibration of a USCT system was chosen as the main topic for this dissertation. The dissertation thesis presents novel methods in the area of reconstruction of attenuation images, sensitivity calibration, and mainly geometrical calibration. The methods were implemented and tested on real data generated by the Karlsruhe USCT device.

Advanced VLBI Imaging

Very Long Baseline Interferometry (VLBI) is an observational technique developed in astronomy for combining multiple radio telescopes into a single virtual instrument with an effective aperture reaching up to many thousand kilometers and enabling measurements at highest angular resolutions. The celebrated examples of applying VLBI to astrophysical studies include detailed, high-resolution images of the innermost parts of relativistic outflows (jets) in active galactic nuclei (AGN) and recent pioneering observations of the shadows of supermassive black holes (SMBH) in the center of our Galaxy and in the galaxy M87. Despite these and many other proven successes of VLBI, analysis and imaging of VLBI data still remain difficult, owing in part to the fact that VLBI imaging inherently constitutes an ill-posed inverse problem. Historically, this problem has been addressed in radio interferometry by the CLEAN algorithm, a matching-pursuit inverse modeling method developed in the early 1970-s and since then established as a de-facto standard approach for imaging VLBI data. In recent years, the constantly increasing demand for improving quality and fidelity of interferometric image reconstruction has resulted in several attempts to employ new approaches, such as forward modeling and Bayesian estimation, for application to VLBI imaging. While the current state-of-the-art forward modeling and Bayesian techniques may outperform CLEAN in terms of accuracy, resolution, robustness, and adaptability, they also tend to require more complex structure and longer computation times, and rely on extensive finetuning of a larger number of non-trivial hyperparameters. This leaves an ample room for further searches for potentially more effective imaging approaches and provides the main motivation for this dissertation and its particular focusing on the need to unify algorithmic frameworks and to study VLBI imaging from the perspective of inverse problems in general. In pursuit of this goal, and based on an extensive qualitative comparison of the existing methods, this dissertation comprises the development, testing, and first implementations of two novel concepts for improved interferometric image reconstruction. The concepts combine the known benefits of current forward modeling techniques, develop more automatic and less supervised algorithms for image reconstruction, and realize them within two different frameworks. The first framework unites multiscale imaging algorithms in the spirit of compressive sensing with a dictionary adapted to the uv-coverage and its defects (DoG-HiT, DoB-CLEAN). We extend this approach to dynamical imaging and polarimetric imaging. The core components of this framework are realized in a multidisciplinary and multipurpose software MrBeam, developed as part of this dissertation. The second framework employs a multiobjective genetic evolutionary algorithm (MOEA/D) for the purpose of achieving fully unsupervised image reconstruction and hyperparameter optimization. These new methods are shown to outperform the existing methods in various metrics such as angular resolution, structural sensitivity, and degree of supervision. We demonstrate the great potential of these new techniques with selected applications to frontline VLBI observations of AGN jets and SMBH. In addition to improving the quality and robustness of image reconstruction, DoG-HiT, DoB-CLEAN and MOEA/D also provide such novel capabilities as dynamic reconstruction of polarimetric images on minute time-scales, or near-real time and unsupervised data analysis (useful in particular for application to large imaging surveys). The techniques and software developed in this dissertation are of interest for a wider range of inverse problems as well. This includes such versatile fields such as Ly-alpha tomography (where we improve estimates of the thermal state of the intergalactic medium), the cosmographic search for dark matter (where we improve forecasted bounds on ultralight dilatons), medical imaging, and solar spectroscopy

Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery

One of the main challenges for computer-assisted surgery (CAS) is to determine the intra-opera- tive morphology and motion of soft-tissues. This information is prerequisite to the registration of multi-modal patient-specific data for enhancing the surgeon’s navigation capabilites by observ- ing beyond exposed tissue surfaces and for providing intelligent control of robotic-assisted in- struments. In minimally invasive surgery (MIS), optical techniques are an increasingly attractive approach for in vivo 3D reconstruction of the soft-tissue surface geometry. This paper reviews the state-of-the-art methods for optical intra-operative 3D reconstruction in laparoscopic surgery and discusses the technical challenges and future perspectives towards clinical translation. With the recent paradigm shift of surgical practice towards MIS and new developments in 3D opti- cal imaging, this is a timely discussion about technologies that could facilitate complex CAS procedures in dynamic and deformable anatomical regions