Evolutionary Models for Signal Enhancement and Approximation

This thesis deals with nature-inspired evolution processes for the purpose of signal enhancement and approximation. The focus lies on mathematical models which originate from the description of swarm behaviour. We extend existing approaches and show the potential of swarming processes as a modelling tool in image processing. In our work, we discuss the use cases of grey scale quantisation, contrast enhancement, line detection, and coherence enhancement. Furthermore, we propose a new and purely repulsive model of swarming that turns out to describe a specific type of backward diffusion process. It is remarkable that our model provides extensive stability guarantees which even support the utilisation of standard numerics. In experiments, we demonstrate its applicability to global and local contrast enhancement of digital images. In addition, we study the problem of one-dimensional signal approximation with limited resources using an adaptive sampling approach including tonal optimisation. We suggest a direct energy minimisation strategy and validate its efficacy in experiments. Moreover, we show that our approximation model can outperform a method recently proposed by Dar and Bruckstein

Nonlocal evolutions in image processing

The main topic of this thesis is to study a general framework which encompasses a wide class of nonlocal filters. For that matter, we introduce a general initial value problem, defined in terms of integro-differential equations and following the work of Weickert, we impose a set of basic assumptions that turn it into a well-posed model and develop nonlocal scale-space theory. Moreover, we go one step further and consider the consequences of relaxing some of this initial set of requirements. With each particular modification of the initial requirements, we obtain a particular framework which encompasses a more specific, yet wide, family of nonlocal processes.Das Hauptthema dieser Arbeit ist die Untersuchung eines allgemeinen Rahmens für eine breite Klasse nichtlokaler Filter. Zuerst führen wir ein Modell ein, das auf Integro-Differentialgleichungen basiert. Wir ergänzen es mit einer Reihe von Grundannahmen, die es uns ermöglichen, eine nichtlokale Skalenraumtheorie zu entwickeln, wie in [1]. Außerdem betrachten wir die Konsequenzen der Abschwächung einiger dieser Annahmen. Wir stellen verschiedene Beispiele für die mit jeder Relaxation erhaltenen Prozesse vor

Advanced Techniques for Ground Penetrating Radar Imaging

Ground penetrating radar (GPR) has become one of the key technologies in subsurface sensing and, in general, in non-destructive testing (NDT), since it is able to detect both metallic and nonmetallic targets. GPR for NDT has been successfully introduced in a wide range of sectors, such as mining and geology, glaciology, civil engineering and civil works, archaeology, and security and defense. In recent decades, improvements in georeferencing and positioning systems have enabled the introduction of synthetic aperture radar (SAR) techniques in GPR systems, yielding GPR–SAR systems capable of providing high-resolution microwave images. In parallel, the radiofrequency front-end of GPR systems has been optimized in terms of compactness (e.g., smaller Tx/Rx antennas) and cost. These advances, combined with improvements in autonomous platforms, such as unmanned terrestrial and aerial vehicles, have fostered new fields of application for GPR, where fast and reliable detection capabilities are demanded. In addition, processing techniques have been improved, taking advantage of the research conducted in related fields like inverse scattering and imaging. As a result, novel and robust algorithms have been developed for clutter reduction, automatic target recognition, and efficient processing of large sets of measurements to enable real-time imaging, among others. This Special Issue provides an overview of the state of the art in GPR imaging, focusing on the latest advances from both hardware and software perspectives

Feature-preserving image restoration and its application in biological fluorescence microscopy

This thesis presents a new investigation of image restoration and its application to fluorescence cell microscopy. The first part of the work is to develop advanced image denoising algorithms to restore images from noisy observations by using a novel featurepreserving diffusion approach. I have applied these algorithms to different types of images, including biometric, biological and natural images, and demonstrated their superior performance for noise removal and feature preservation, compared to several state of the art methods. In the second part of my work, I explore a novel, simple and inexpensive super-resolution restoration method for quantitative microscopy in cell biology. In this method, a super-resolution image is restored, through an inverse process, by using multiple diffraction-limited (low) resolution observations, which are acquired from conventional microscopes whilst translating the sample parallel to the image plane, so referred to as translation microscopy (TRAM). A key to this new development is the integration of a robust feature detector, developed in the first part, to the inverse process to restore high resolution images well above the diffraction limit in the presence of strong noise. TRAM is a post-image acquisition computational method and can be implemented with any microscope. Experiments show a nearly 7-fold increase in lateral spatial resolution in noisy biological environments, delivering multi-colour image resolution of ~30 nm

Coronary Artery Segmentation and Motion Modelling

Conventional coronary artery bypass surgery requires invasive sternotomy and the use of a cardiopulmonary bypass, which leads to long recovery period and has high infectious potential. Totally endoscopic coronary artery bypass (TECAB) surgery based on image guided robotic surgical approaches have been developed to allow the clinicians to conduct the bypass surgery off-pump with only three pin holes incisions in the chest cavity, through which two robotic arms and one stereo endoscopic camera are inserted. However, the restricted field of view of the stereo endoscopic images leads to possible vessel misidentification and coronary artery mis-localization. This results in 20-30% conversion rates from TECAB surgery to the conventional approach. We have constructed patient-specific 3D + time coronary artery and left ventricle motion models from preoperative 4D Computed Tomography Angiography (CTA) scans. Through temporally and spatially aligning this model with the intraoperative endoscopic views of the patient's beating heart, this work assists the surgeon to identify and locate the correct coronaries during the TECAB precedures. Thus this work has the prospect of reducing the conversion rate from TECAB to conventional coronary bypass procedures. This thesis mainly focus on designing segmentation and motion tracking methods of the coronary arteries in order to build pre-operative patient-specific motion models. Various vessel centreline extraction and lumen segmentation algorithms are presented, including intensity based approaches, geometric model matching method and morphology-based method. A probabilistic atlas of the coronary arteries is formed from a group of subjects to facilitate the vascular segmentation and registration procedures. Non-rigid registration framework based on a free-form deformation model and multi-level multi-channel large deformation diffeomorphic metric mapping are proposed to track the coronary motion. The methods are applied to 4D CTA images acquired from various groups of patients and quantitatively evaluated

Wave-equation based seismic multiple attenuation

Reflection seismology is widely used to map the subsurface geological structure of the Earth. Seismic multiples can contaminate seismic data and are therefore due to be removed. For seismic multiple attenuation, wave-equation based methods are proved to be effective in most cases, which involve two aspects: multiple prediction and multiple subtraction. Targets of both aspects are to develop and apply a fully datadriven algorithm for multiple prediction, and a robust technique for multiple subtraction. Based on many schemes developed by others regarding to the targets, this thesis addresses and tackles the problems of wave-equation based seismic multiple attenuation by several approaches. First, the issue of multiple attenuation in land seismic data is discussed. Multiple Prediction through Inversion (MPTI) method is expanded to be applied in the poststack domain and in the CMP domain to handle the land data with low S/N ratio, irregular geometry and missing traces. A running smooth filter and an adaptive threshold K-NN (nearest neighbours) filter are proposed to help to employ MPTI on land data in the shot domain. Secondly, the result of multiple attenuation depends much upon the effectiveness of the adaptive subtraction. The expanded multi-channel matching (EMCM) filter is proved to be effective. In this thesis, several strategies are discussed to improve the result of EMCM. Among them, to model and subtract the multiples according to their orders is proved to be practical in enhancing the effect of EMCM, and a masking filter is adopted to preserve the energy of primaries. Moreover, an iterative application of EMCM is proposed to give the optimized result. Thirdly, with the limitation of current 3D seismic acquisition geometries, the sampling in the crossline direction is sparse. This seriously affects the application of the 3D multiple attenuation. To tackle the problem, a new approach which applies a trajectory stacking Radon transform along with the energy spectrum is proposed in this thesis. It can replace the time-consuming time-domain sparse inversion with similar effectiveness and much higher efficiency. Parallel computing is discussed in the thesis so as to enhance the efficiency of the strategies. The Message-Passing Interface (MPI) environment is implemented in most of the algorithms mentioned above and greatly improves the efficiency