Mathematics and Algorithms in Tomography

This is the eighth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, sonar, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, vector tomography, and texture analysis

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Acoustic tomography imaging for atmospheric temperature and wind velocity field reconstruction

Owing to its non-invasive nature, fast imaging speed, low equipment cost, scalability for a variety of measurement ranges, and ability to simultaneously monitor both temperature and wind velocity fields, acoustic tomography has attracted considerable interest in the field of atmospheric imaging. This thesis aims to improve the reconstruction quality of the acoustic tomography system for temperature and wind velocity field imaging. Focusing on this goal, the contribution of the thesis can be summarised from the perspectives of data collection system development, robust and accurate TOF estimation method, and high-quality scalar and vector tomographic image reconstruction methods for temperature and wind velocity fields respectively. Details are given below. Firstly, in order to facilitate the experimental study of acoustic tomography imaging, the design and evaluation of the data collection system and TOF estimation method was presented. The evaluation results indicate that the presented data acquisition system and TOF estimation method has good quantitative accuracy in the lab-scale experiments. The temporal resolution is of great significance for the real-time monitoring of the fast-changing temperature field. To improve the temporal resolution, a novel online time-resolved reconstruction (OTRR) method is presented, which can reconstruct high quality time-resolved images by using fewer TOFs per frame. Compared to state-of-the-art dynamic reconstruction algorithms such as the Kalman filter reconstruction, the proposed algorithm demonstrated superior spatial resolution and preferable quantitative accuracy in the reconstructed images. These features are necessary for the real-time monitoring of the fast-changing temperature field. The forward modelling of most acoustic tomography problems is based on a straight ray model, which may result in large modelling errors due to the refraction effect under a large gradient temperature field. In order to reduce the inaccuracy of using the straight ray model, a bent ray model and nonlinear reconstruction algorithm is applied, which allows the sound propagation ray paths and temperature distribution to be reconstructed iteratively from the TOFs. Using acoustic tomography to reconstruct large-scale temperature and wind velocity fields, a fully parallel TOF measurement scheme is necessary. To achieve this goal, a set of orthogonal acoustic waveforms based on the filtered and modulated Kasami sequence is designed and a cross-correlation based TOF estimation method is used for data collection. Besides, to overcome the invisible field problem and improve the image quality of the wind velocity reconstruction, a divergence-free regularised vector tomographic reconstruction algorithm is studied. The proposed method is able to provide accurate tomographic reconstruction of the 2D horizontal wind velocity field from the TOF measurements. In summary, this thesis focuses on the improvement of acoustic tomography techniques for temperature and wind velocity fields, including the phase corrected Akaike information criterion (AIC) TOF estimation for accurate and robust TOF estimation, the online time-resolved reconstruction method for real-time monitoring of the fast changing temperature field, the nonlinear reconstruction based on the bent ray model to reconstruct the temperature field with a large gradient, and the divergence-free regularised reconstruction method to visualise the 2D horizontal wind velocity field

Mathematical Methods in Tomography

This is the seventh Oberwolfach conference on the mathematics of tomography, the first one taking place in 1980. Tomography is the most popular of a series of medical and scientific imaging techniques that have been developed since the mid seventies of the last century

Chapter Machine Learning in Volcanology: A Review

A volcano is a complex system, and the characterization of its state at any given time is not an easy task. Monitoring data can be used to estimate the probability of an unrest and/or an eruption episode. These can include seismic, magnetic, electromagnetic, deformation, infrasonic, thermal, geochemical data or, in an ideal situation, a combination of them. Merging data of different origins is a non-trivial task, and often even extracting few relevant and information-rich parameters from a homogeneous time series is already challenging. The key to the characterization of volcanic regimes is in fact a process of data reduction that should produce a relatively small vector of features. The next step is the interpretation of the resulting features, through the recognition of similar vectors and for example, their association to a given state of the volcano. This can lead in turn to highlight possible precursors of unrests and eruptions. This final step can benefit from the application of machine learning techniques, that are able to process big data in an efficient way. Other applications of machine learning in volcanology include the analysis and classification of geological, geochemical and petrological “static” data to infer for example, the possible source and mechanism of observed deposits, the analysis of satellite imagery to quickly classify vast regions difficult to investigate on the ground or, again, to detect changes that could indicate an unrest. Moreover, the use of machine learning is gaining importance in other areas of volcanology, not only for monitoring purposes but for differentiating particular geochemical patterns, stratigraphic issues, differentiating morphological patterns of volcanic edifices, or to assess spatial distribution of volcanoes. Machine learning is helpful in the discrimination of magmatic complexes, in distinguishing tectonic settings of volcanic rocks, in the evaluation of correlations of volcanic units, being particularly helpful in tephrochronology, etc. In this chapter we will review the relevant methods and results published in the last decades using machine learning in volcanology, both with respect to the choice of the optimal feature vectors and to their subsequent classification, taking into account both the unsupervised and the supervised approaches

Robust inversion and detection techniques for improved imaging performance

Thesis (Ph.D.)--Boston UniversityIn this thesis we aim to improve the performance of information extraction from imaging systems through three thrusts. First, we develop improved image formation methods for physics-based, complex-valued sensing problems. We propose a regularized inversion method that incorporates prior information about the underlying field into the inversion framework for ultrasound imaging. We use experimental ultrasound data to compute inversion results with the proposed formulation and compare it with conventional inversion techniques to show the robustness of the proposed technique to loss of data. Second, we propose methods that combine inversion and detection in a unified framework to improve imaging performance. This framework is applicable for cases where the underlying field is label-based such that each pixel of the underlying field can only assume values from a discrete, limited set. We consider this unified framework in the context of combinatorial optimization and propose graph-cut based methods that would result in label-based images, thereby eliminating the need for a separate detection step. Finally, we propose a robust method of object detection from microscopic nanoparticle images. In particular, we focus on a portable, low cost interferometric imaging platform and propose robust detection algorithms using tools from computer vision. We model the electromagnetic image formation process and use this model to create an enhanced detection technique. The effectiveness of the proposed technique is demonstrated using manually labeled ground-truth data. In addition, we extend these tools to develop a detection based autofocusing algorithm tailored for the high numerical aperture interferometric microscope

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