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.

SPHERA, a new Italian convection-permitting regional reanalysis: improving heavy-rainfall representation and describing hail-prone environments

Extreme weather events related to deep convection are high-impact critical phenomena whose reliable numerical simulation is still challenging. High-resolution (convection-permitting) modeling setups allow to switch off physical parameterizations accountable for substantial errors in convection representation. A new convection-permitting reanalysis over Italy (SPHERA) has been produced at ARPAE to enhance the representation and understanding of extreme weather situations. SPHERA is obtained through a dynamical downscaling of the global reanalysis ERA5 using the non-hydrostatic model COSMO at 2.2 km grid spacing over 1995-2020. This thesis aims to verify the expectations placed on SPHERA by analyzing two weather phenomena that are particularly challenging to simulate: heavy rainfall and hail. A quantitative statistical analysis over Italy during 2003-2017 for daily and hourly precipitation is presented to compare the performance of SPHERA with its driver ERA5 considering the national network of rain gauges as reference. Furthermore, two extreme precipitation events are deeply investigated. SPHERA shows a quantitative added skill over ERA5 for moderate to severe and rapid accumulations in terms of adherence to the observations, higher detailing of the spatial fields, and more precise temporal matching. These results prompted the use of SPHERA for the investigation of hailstorms, for which the combination of multiple information is crucial to reduce the substantial uncertainties permeating their understanding. A proxy for hail is developed by combining hail-favoring environmental numerical predictors with observations of ESWD hail reports and satellite overshooting top detections. The procedure is applied to the extended summer season (April-October) of 2016-2018 over the whole SPHERA spatial domain. The results indicate maximum hail likelihood over pre-Alpine regions and the northern Adriatic sea around 15 UTC in June-July, in agreement with recent European hail climatologies. The method demonstrates enhanced performance in case of severe hail occurrences and the ability to separate between ambient signatures depending on hail severity.

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.

Interpreting Judgements using Knowledge Representation Methods and Computational Models of Argument

The goal of the present research is to define a Semantic Web framework for precedent modelling, by using knowledge extracted from text, metadata, and rules, while maintaining a strong text-to-knowledge morphism between legal text and legal concepts, in order to fill the gap between legal document and its semantics. The framework is composed of four different models that make use of standard languages from the Semantic Web stack of technologies: a document metadata structure, modelling the main parts of a judgement, and creating a bridge between a text and its semantic annotations of legal concepts; a legal core ontology, modelling abstract legal concepts and institutions contained in a rule of law; a legal domain ontology, modelling the main legal concepts in a specific domain concerned by case-law; an argumentation system, modelling the structure of argumentation. The input to the framework includes metadata associated with judicial concepts, and an ontology library representing the structure of case-law. The research relies on the previous efforts of the community in the field of legal knowledge representation and rule interchange for applications in the legal domain, in order to apply the theory to a set of real legal documents, stressing the OWL axioms definitions as much as possible in order to enable them to provide a semantically powerful representation of the legal document and a solid ground for an argumentation system using a defeasible subset of predicate logics. It appears that some new features of OWL2 unlock useful reasoning features for legal knowledge, especially if combined with defeasible rules and argumentation schemes. The main task is thus to formalize legal concepts and argumentation patterns contained in a judgement, with the following requirement: to check, validate and reuse the discourse of a judge - and the argumentation he produces - as expressed by the judicial text.

Learning from errors: Psychological, relational, and cultural aspects

Although errors might foster learning, they can also be perceived as something to avoid if they are associated with negative consequences (e.g., receiving a bad grade or being mocked by classmates). Such adverse perceptions may trigger negative emotions and error-avoidance attitudes, limiting the possibility to use errors for learning. These students’ reactions may be influenced by relational and cultural aspects of errors that characterise the learning environment. Accordingly, the main aim of this research was to investigate whether relational and cultural characteristics associated with errors affect psychological mechanisms triggered by making mistakes. In the theoretical part, we described the role of errors in learning using an integrated multilevel (i.e., psychological, relational, and cultural levels of analysis) approach. Then, we presented three studies that analysed how cultural and relational error-related variables affect psychological aspects. The studies adopted a specific empirical methodology (i.e., qualitative, experimental, and correlational) and investigated different samples (i.e., teachers, primary school pupils and middle school students). Findings of study one (cultural level) highlighted errors acquire different meanings that are associated with different teachers’ error-handling strategies (e.g., supporting or penalising errors). Study two (relational level) demonstrated that teachers’ supportive error-handling strategies promote students’ perceptions of being in a positive error climate. Findings of study three (relational and psychological level) showed that positive error climate foster students’ adaptive reactions towards errors and learning outcomes. Overall, our findings indicated that different variables influence students’ learning from errors process and teachers play an important role in conveying specific meanings of errors during learning activities, dealing with students’ mistakes supportively, and establishing an error-friendly classroom environment.