Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.

Coordination and Control of Autonomous Mobile Robots Swarms by using Particle Swarm Optimization Algorithm and Consensus Theory

This thesis presents some different techniques designed to drive a swarm of robots in an a-priori unknown environment in order to move the group from a starting area to a final one avoiding obstacles. The presented techniques are based on two different theories used alone or in combination: Swarm Intelligence (SI) and Graph Theory. Both theories are based on the study of interactions between different entities (also called agents or units) in Multi- Agent Systems (MAS). The first one belongs to the Artificial Intelligence context and the second one to the Distributed Systems context. These theories, each one from its own point of view, exploit the emergent behaviour that comes from the interactive work of the entities, in order to achieve a common goal. The features of flexibility and adaptability of the swarm have been exploited with the aim to overcome and to minimize difficulties and problems that can affect one or more units of the group, having minimal impact to the whole group and to the common main target. Another aim of this work is to show the importance of the information shared between the units of the group, such as the communication topology, because it helps to maintain the environmental information, detected by each single agent, updated among the swarm. Swarm Intelligence has been applied to the presented technique, through the Particle Swarm Optimization algorithm (PSO), taking advantage of its features as a navigation system. The Graph Theory has been applied by exploiting Consensus and the application of the agreement protocol with the aim to maintain the units in a desired and controlled formation. This approach has been followed in order to conserve the power of PSO and to control part of its random behaviour with a distributed control algorithm like Consensus.

Métamorphoses de l'Image des Tartares dans la littérature européenne du XXème siècle

Ce travail doctoral analyse le changement de l’image des Tartares dans la littérature européenne en langue allemande, anglaise, française et italienne du XXe siècle par l’étude de trois figures : la horde mongole, Gengis-khan et Khoubilaï-khan. Il soutient la thèse que, grâce à quelques facteurs historico-culturels comme la remise en question du concept de barbarie, l’essor des totalitarismes, l’ouverture de la Mongolie vers l’Occident, la redécouverte de l’Histoire secrète des Mongols et la fortune de Le divisament dou monde, au cours du XXe siècle, l’image littéraire des gengiskhanides de négative devient positive. Cette étude se compose d’une introduction, de trois chapitres et d’une conclusion. Dans l’introduction, on analyse la formation de l’image des Tartares et son évolution jusqu’à la fin du XIXe siècle, on retrace les facteurs historico-culturels qui la remettent au goût du jour et en provoquent le changement au XXe siècle et on présente le travail. Dans le premier chapitre, on se penche sur la prosopographie des Tartares dans les textes littéraires du XXe siècle, en la confrontant avec leur représentation dans l’art contemporain. Dans le deuxième chapitre, on étudie la façon des Tartares de se rapporter aux autres au sein de la société dans les textes littéraires du XXe siècle. Dans le troisième chapitre, on examine les lieux des gengiskhanides dans les textes littéraires du XXe siècle. Enfin, dans la conclusion, les données acquises au moyen de l’analyse conduite sont confrontées et interprétées. Le changement de l’image des Tartares va de pair avec une Europe qui, après avoir fait l’expérience de deux guerres mondiales, avoir assisté aux revendications de la décolonisation et avoir introjecté la thèse freudienne du « malaise dans la civilisation », remet en discussion sa façon de concevoir la barbarie et l’Altérité.

The Making of a Shiite Bourgeoisie in Lebanon Political Mobilisation, Economic Resources and Formation of a Social Group

The thesis analyses the making of the Shiite middle- and upper/entrepreneurial-class in Lebanon from the 1960s till the present day. The trajectory explores the historical, political and social (internal and external) factors that brought a sub-proletariat to mobilise and become an entrepreneurial bourgeoisie in the span of less than three generations. This work proposes the main theoretical hypothesis to unpack and reveal the trajectory of a very recent social class that through education, diaspora, political and social mobilisation evolved in a few years into a very peculiar bourgeoisie: whereas Christian-Maronite middle class practically produced political formations and benefited from them and from Maronite’s state supremacy (National Pact, 1943) reinforcing the community’s status quo, Shiites built their own bourgeoisie from within, and mobilised their “cadres” (Boltanski) not just to benefit from their renovated presence at the state level, but to oppose to it. The general Social Movement Theory (SMT), as well as a vast amount of the literature on (middle) class formation are therefore largely contradicted, opening up new territories for discussion on how to build a bourgeoisie without the state’s support (Social Mobilisation Theory, Resource Mobilisation Theory) and if, eventually, the middle class always produces democratic movements (the emergence of a social group out of backwardness and isolation into near dominance of a political order). The middle/upper class described here is at once an economic class related to the control of multiple forms of capital, and produced by local, national, and transnational networks related to flows of services, money, and education, and a culturally constructed social location and identity structured by economic as well as other forms of capital in relation to other groups in Lebanon.

Regularization meets GreenAI: a new framework for image reconstruction in life sciences applications

Ill-conditioned inverse problems frequently arise in life sciences, particularly in the context of image deblurring and medical image reconstruction. These problems have been addressed through iterative variational algorithms, which regularize the reconstruction by adding prior knowledge about the problem's solution. Despite the theoretical reliability of these methods, their practical utility is constrained by the time required to converge. Recently, the advent of neural networks allowed the development of reconstruction algorithms that can compute highly accurate solutions with minimal time demands. Regrettably, it is well-known that neural networks are sensitive to unexpected noise, and the quality of their reconstructions quickly deteriorates when the input is slightly perturbed. Modern efforts to address this challenge have led to the creation of massive neural network architectures, but this approach is unsustainable from both ecological and economic standpoints. The recently introduced GreenAI paradigm argues that developing sustainable neural network models is essential for practical applications. In this thesis, we aim to bridge the gap between theory and practice by introducing a novel framework that combines the reliability of model-based iterative algorithms with the speed and accuracy of end-to-end neural networks. Additionally, we demonstrate that our framework yields results comparable to state-of-the-art methods while using relatively small, sustainable models. In the first part of this thesis, we discuss the proposed framework from a theoretical perspective. We provide an extension of classical regularization theory, applicable in scenarios where neural networks are employed to solve inverse problems, and we show there exists a trade-off between accuracy and stability. Furthermore, we demonstrate the effectiveness of our methods in common life science-related scenarios. In the second part of the thesis, we initiate an exploration extending the proposed method into the probabilistic domain. We analyze some properties of deep generative models, revealing their potential applicability in addressing ill-posed inverse problems.