Variational and learning models for image and time series inverse problems

Inverse problems are at the core of many challenging applications. Variational and learning models provide estimated solutions of inverse problems as the outcome of specific reconstruction maps. In the variational approach, the result of the reconstruction map is the solution of a regularized minimization problem encoding information on the acquisition process and prior knowledge on the solution. In the learning approach, the reconstruction map is a parametric function whose parameters are identified by solving a minimization problem depending on a large set of data. In this thesis, we go beyond this apparent dichotomy between variational and learning models and we show they can be harmoniously merged in unified hybrid frameworks preserving their main advantages. We develop several highly efficient methods based on both these model-driven and data-driven strategies, for which we provide a detailed convergence analysis. The arising algorithms are applied to solve inverse problems involving images and time series. For each task, we show the proposed schemes improve the performances of many other existing methods in terms of both computational burden and quality of the solution. In the first part, we focus on gradient-based regularized variational models which are shown to be effective for segmentation purposes and thermal and medical image enhancement. We consider gradient sparsity-promoting regularized models for which we develop different strategies to estimate the regularization strength. Furthermore, we introduce a novel gradient-based Plug-and-Play convergent scheme considering a deep learning based denoiser trained on the gradient domain. In the second part, we address the tasks of natural image deblurring, image and video super resolution microscopy and positioning time series prediction, through deep learning based methods. We boost the performances of supervised, such as trained convolutional and recurrent networks, and unsupervised deep learning strategies, such as Deep Image Prior, by penalizing the losses with handcrafted regularization terms.

Integrated communication and learning towards autonomous mobile radio networks

The integration of distributed and ubiquitous intelligence has emerged over the last years as the mainspring of transformative advancements in mobile radio networks. As we approach the era of “mobile for intelligence”, next-generation wireless networks are poised to undergo significant and profound changes. Notably, the overarching challenge that lies ahead is the development and implementation of integrated communication and learning mechanisms that will enable the realization of autonomous mobile radio networks. The ultimate pursuit of eliminating human-in-the-loop constitutes an ambitious challenge, necessitating a meticulous delineation of the fundamental characteristics that artificial intelligence (AI) should possess to effectively achieve this objective. This challenge represents a paradigm shift in the design, deployment, and operation of wireless networks, where conventional, static configurations give way to dynamic, adaptive, and AI-native systems capable of self-optimization, self-sustainment, and learning. This thesis aims to provide a comprehensive exploration of the fundamental principles and practical approaches required to create autonomous mobile radio networks that seamlessly integrate communication and learning components. The first chapter of this thesis introduces the notion of Predictive Quality of Service (PQoS) and adaptive optimization and expands upon the challenge to achieve adaptable, reliable, and robust network performance in dynamic and ever-changing environments. The subsequent chapter delves into the revolutionary role of generative AI in shaping next-generation autonomous networks. This chapter emphasizes achieving trustworthy uncertainty-aware generation processes with the use of approximate Bayesian methods and aims to show how generative AI can improve generalization while reducing data communication costs. Finally, the thesis embarks on the topic of distributed learning over wireless networks. Distributed learning and its declinations, including multi-agent reinforcement learning systems and federated learning, have the potential to meet the scalability demands of modern data-driven applications, enabling efficient and collaborative model training across dynamic scenarios while ensuring data privacy and reducing communication overhead.

Population ageing, longevity and migration: an overlapping generations approach

The silent demographic revolution characterizing the main industrialized countries is an unavoidable factor which has major economic, social, cultural and psychological implications. This thesis studies the main consequences of population ageing and the connections with the phenomenon of migration, The theoretical analysis is developed using Overlapping Generations Models (OLG). The thesis is divided in the following four chapters: 1) “A Model for Determining Consumption and Social Assistance Demand in Uncertainty Conditions”, focuses on the relation between demographic impact and social insurance and proposes the institution of a non selfsufficiency fund for the elderly. 2) "Population Ageing, Longevity and Health", analyzes the effects of health investment on intertemporal individual behaviour and capital accumulation. 3) "Population Ageing and the Nursing Flow", studies the consequences of migration in the nursing sector. 4) "Quality of Multiculturalism and Minorities' Assimilation", focuses on the problem of assimilation and integration of minorities.

The elderly health status and its correlation with ageing biomarkers: the European Project Mark-Age

According to the latest statistics projections formulated by Eurostat, the proportion of elderly EU-27’s population aged over 65 years old is predicted to increase from 17.5 % in 2011 to 29.5 % by 2060. This "population explosion" makes extremely important to identify the different genetic and molecular mechanisms which underpin the morbidity and mortality along with new strategies able to counteract or slow down its progress. In this scenario fits the European Project MARK-AGE whose aim was to identify a robust set of biomarkers of human ageing able to discriminate between chronological and biological ageing and to derive a model for healthy ageing through the analysis of three populations from different European countries, supposed to be characterized by different ageing rate: 1. Subjects representing the “Normal” or “Physiological” aging. 2. Subjects representing the “successful” or “decelerate” aging 3. Subjects representing the “accelerated” aging. The aim of this work was to recruit and characterize volunteers, to perform an accurate analysis of the health status of elderly recruited subjects (60-79 years) verifying any possible dissimilarity in their aging trajectories, to identify a set of robust ageing biomarkers and investigate possible correlations between ageing biomarkers and health status of recruited volunteers. The model proposed by MARK-AGE Project regarding different ageing trajectories has been confirmed and several ageing biomarkers have been identified.