Regularization methods for the solution of a nonlinear least-squares problem in tomography

In this work we study a polyenergetic and multimaterial model for the breast image reconstruction in Digital Tomosynthesis, taking into consideration the variety of the materials forming the object and the polyenergetic nature of the X-rays beam. The modelling of the problem leads to the resolution of a high-dimensional nonlinear least-squares problem that, due to its nature of inverse ill-posed problem, needs some kind of regularization. We test two main classes of methods: the Levenberg-Marquardt method (together with the Conjugate Gradient method for the computation of the descent direction) and two limited-memory BFGS-like methods (L-BFGS). We perform some experiments for different values of the regularization parameter (constant or varying at each iteration), tolerances and stop conditions. Finally, we analyse the performance of the several methods comparing relative errors, iterations number, times and the qualities of the reconstructed images.

Compressed sensing in digital tomosynthesis reconstruction

In this work we study a model for the breast image reconstruction in Digital Tomosynthesis, that is a non-invasive and non-destructive method for the three-dimensional visualization of the inner structures of an object, in which the data acquisition includes measuring a limited number of low-dose two-dimensional projections of an object by moving a detector and an X-ray tube around the object within a limited angular range. The problem of reconstructing 3D images from the projections provided in the Digital Tomosynthesis is an ill-posed inverse problem, that leads to a minimization problem with an object function that contains a data fitting term and a regularization term. The contribution of this thesis is to use the techniques of the compressed sensing, in particular replacing the standard least squares problem of data fitting with the problem of minimizing the 1-norm of the residuals, and using as regularization term the Total Variation (TV). We tested two different algorithms: a new alternating minimization algorithm (ADM), and a version of the more standard scaled projected gradient algorithm (SGP) that involves the 1-norm. We perform some experiments and analyse the performance of the two methods comparing relative errors, iterations number, times and the qualities of the reconstructed images. In conclusion we noticed that the use of the 1-norm and the Total Variation are valid tools in the formulation of the minimization problem for the image reconstruction resulting from Digital Tomosynthesis and the new algorithm ADM has reached a relative error comparable to a version of the classic algorithm SGP and proved best in speed and in the early appearance of the structures representing the masses.

Mac protocols for linear wireless (sensor) networks

Wireless sensor networks (WSNs) consist of a large number of sensor nodes, characterized by low power constraint, limited transmission range and limited computational capabilities [1][2].The cost of these devices is constantly decreasing, making it possible to use a large number of sensor devices in a wide array of commercial, environmental, military, and healthcare fields. Some of these applications involve placing the sensors evenly spaced on a straight line for example in roads, bridges, tunnels, water catchments and water pipelines, city drainages, oil and gas pipelines etc., making a special class of these networks which we define as a Linear Wireless Network (LWN). In LWNs, data transmission happens hop by hop from the source to the destination, through a route composed of multiple relays. The peculiarity of the topology of LWNs, motivates the design of specialized protocols, taking advantage of the linearity of such networks, in order to increase reliability, communication efficiency, energy savings, network lifetime and to minimize the end-to-end delay [3]. In this thesis a novel contention based Medium Access Control (MAC) protocol called L-CSMA, specifically devised for LWNs is presented. The basic idea of L-CSMA is to assign different priorities to nodes based on their position along the line. The priority is assigned in terms of sensing duration, whereby nodes closer to the destination are assigned shorter sensing time compared to the rest of the nodes and hence higher priority. This mechanism speeds up the transmission of packets which are already in the path, making transmission flow more efficient. Using NS-3 simulator, the performance of L-CSMA in terms of packets success rate, that is, the percentage of packets that reach destination, and throughput are compared with that of IEEE 802.15.4 MAC protocol, de-facto standard for wireless sensor networks. In general, L-CSMA outperforms the IEEE 802.15.4 MAC protocol.

Galactic fountain flows in high-resolution hydrodynamical simulations of galaxy disks

Feedback from the most massive components of a young stellar cluster deeply affects the surrounding ISM driving an expanding over-pressured hot gas cavity in it. In spiral galaxies these structures may have sufficient energy to break the disk and eject large amount of material into the halo. The cycling of this gas, which eventually will fall back onto the disk, is known as galactic fountains. We aim at better understanding the dynamics of such fountain flow in a Galactic context, frame the problem in a more dynamic environment possibly learning about its connection and regulation to the local driving mechanism and understand its role as a metal diffusion channel. The interaction of the fountain with a hot corona is hereby analyzed, trying to understand the properties and evolution of the extraplanar material. We perform high resolution hydrodynamical simulations with the moving-mesh code AREPO to model the multi-phase ISM of a Milky Way type galaxy. A non-equilibrium chemical network is included to self consistently follow the evolution of the main coolants of the ISM. Spiral arm perturbations in the potential are considered so that large molecular gas structures are able to dynamically form here, self shielded from the interstellar radiation field. We model the effect of SN feedback from a new-born stellar cluster inside such a giant molecular cloud, as the driving force of the fountain. Passive Lagrangian tracer particles are used in conjunction to the SN energy deposition to model and study diffusion of freshly synthesized metals. We find that both interactions with hot coronal gas and local ISM properties and motions are equally important in shaping the fountain. We notice a bimodal morphology where most of the ejected gas is in a cold $10^4$ K clumpy state while the majority of the affected volume is occupied by a hot diffuse medium. While only about 20\% of the produced metals stay local, most of them quickly diffuse through this hot regime to great scales.