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.

Assimilation of Meteosat Second Generation (MSG) satellite data in a regional numerical weather prediction model using a one-dimensional variational approach

The quality of temperature and humidity retrievals from the infrared SEVIRI sensors on the geostationary Meteosat Second Generation (MSG) satellites is assessed by means of a one dimensional variational algorithm. The study is performed with the aim of improving the spatial and temporal resolution of available observations to feed analysis systems designed for high resolution regional scale numerical weather prediction (NWP) models. The non-hydrostatic forecast model COSMO (COnsortium for Small scale MOdelling) in the ARPA-SIM operational configuration is used to provide background fields. Only clear sky observations over sea are processed. An optimised 1D–VAR set-up comprising of the two water vapour and the three window channels is selected. It maximises the reduction of errors in the model backgrounds while ensuring ease of operational implementation through accurate bias correction procedures and correct radiative transfer simulations. The 1D–VAR retrieval quality is firstly quantified in relative terms employing statistics to estimate the reduction in the background model errors. Additionally the absolute retrieval accuracy is assessed comparing the analysis with independent radiosonde and satellite observations. The inclusion of satellite data brings a substantial reduction in the warm and dry biases present in the forecast model. Moreover it is shown that the retrieval profiles generated by the 1D–VAR are well correlated with the radiosonde measurements. Subsequently the 1D–VAR technique is applied to two three–dimensional case–studies: a false alarm case–study occurred in Friuli–Venezia–Giulia on the 8th of July 2004 and a heavy precipitation case occurred in Emilia–Romagna region between 9th and 12th of April 2005. The impact of satellite data for these two events is evaluated in terms of increments in the integrated water vapour and saturation water vapour over the column, in the 2 meters temperature and specific humidity and in the surface temperature. To improve the 1D–VAR technique a method to calculate flow–dependent model error covariance matrices is also assessed. The approach employs members from an ensemble forecast system generated by perturbing physical parameterisation schemes inside the model. The improved set–up applied to the case of 8th of July 2004 shows a substantial neutral impact.

Analyzing convergence of Agricultural and Rural Areas in the Enlarged EU: The case of Hungary

The fall of the Berlin Wall opened the way for a reform path – the transition process – which accompanied ten former Socialist countries in Central and South Eastern Europe to knock at the EU doors. By the way, at the time of the EU membership several economic and structural weaknesses remained. A tendency towards convergence between the new Member States (NMS) and the EU average income level emerged, together with a spread of inequality at the sub-regional level, mainly driven by the backwardness of the agricultural and rural areas. Several progresses were made in evaluating the policies for rural areas, but a shared definition of rurality is still missing. Numerous indicators were calculated for assessing the effectiveness of the Common Agricultural Policy and Rural Development Policy. Previous analysis on the Central and Eastern European countries found that the characteristics of the most backward areas were insufficiently addressed by the policies enacted; the low data availability and accountability at a sub-regional level, and the deficiencies in institutional planning and implementation represented an obstacle for targeting policies and payments. The next pages aim at providing a basis for understanding the connections between the peculiarities of the transition process, the current development performance of NMS and the EU role, with particular attention to the agricultural and rural areas. Applying a mixed methodological approach (multivariate statistics, non-parametric methods, spatial econometrics), this study contributes to the identification of rural areas and to the analysis of the changes occurred during the EU membership in Hungary, assessing the effect of CAP introduction and its contribution to the convergence of the Hungarian agricultural and rural. The author believes that more targeted – and therefore efficient – policies for agricultural and rural areas require a deeper knowledge of their structural and dynamic characteristics.

Spatial Disparity and Dynamic Trajectory of Convergence in China: Construction and Application of a Composite Index of Regional Development

China is a large country characterized by remarkable growth and distinct regional diversity. Spatial disparity has always been a hot issue since China has been struggling to follow a balanced growth path but still confronting with unprecedented pressures and challenges. To better understand the inequality level benchmarking spatial distributions of Chinese provinces and municipalities and estimate dynamic trajectory of sustainable development in China, I constructed the Composite Index of Regional Development (CIRD) with five sub pillars/dimensions involving Macroeconomic Index (MEI), Science and Innovation Index (SCI), Environmental Sustainability Index (ESI), Human Capital Index (HCI) and Public Facilities Index (PFI), endeavoring to cover various fields of regional socioeconomic development. Ranking reports on the five sub dimensions and aggregated CIRD were provided in order to better measure the developmental degrees of 31 or 30 Chinese provinces and municipalities over 13 years from 1998 to 2010 as the time interval of three “Five-year Plans”. Further empirical applications of this CIRD focused on clustering and convergence estimation, attempting to fill up the gap in quantifying the developmental levels of regional comprehensive socioeconomics and estimating the dynamic convergence trajectory of regional sustainable development in a long run. Four clusters were benchmarked geographically-oriented in the map on the basis of cluster analysis, and club-convergence was observed in the Chinese provinces and municipalities based on stochastic kernel density estimation.

A distributed middleware for IT/OT convergence in modern industrial environments

The modern industrial environment is populated by a myriad of intelligent devices that collaborate for the accomplishment of the numerous business processes in place at the production sites. The close collaboration between humans and work machines poses new interesting challenges that industry must overcome in order to implement the new digital policies demanded by the industrial transition. The Industry 5.0 movement is a companion revolution of the previous Industry 4.0, and it relies on three characteristics that any industrial sector should have and pursue: human centrality, resilience, and sustainability. The application of the fifth industrial revolution cannot be completed without moving from the implementation of Industry 4.0-enabled platforms. The common feature found in the development of this kind of platform is the need to integrate the Information and Operational layers. Our thesis work focuses on the implementation of a platform addressing all the digitization features foreseen by the fourth industrial revolution, making the IT/OT convergence inside production plants an improvement and not a risk. Furthermore, we added modular features to our platform enabling the Industry 5.0 vision. We favored the human centrality using the mobile crowdsensing techniques and the reliability and sustainability using pluggable cloud computing services, combined with data coming from the crowd support. We achieved important and encouraging results in all the domains in which we conducted our experiments. Our IT/OT convergence-enabled platform exhibits the right performance needed to satisfy the strict requirements of production sites. The multi-layer capability of the framework enables the exploitation of data not strictly coming from work machines, allowing a more strict interaction between the company, its employees, and customers.

Inside standard and hyperspectral low-dose CT variational imaging: parameter identification and material decomposition

The main contribution of this thesis is the proposal of novel strategies for the selection of parameters arising in variational models employed for the solution of inverse problems with data corrupted by Poisson noise. In light of the importance of using a significantly small dose of X-rays in Computed Tomography (CT), and its need of using advanced techniques to reconstruct the objects due to the high level of noise in the data, we will focus on parameter selection principles especially for low photon-counts, i.e. low dose Computed Tomography. For completeness, since such strategies can be adopted for various scenarios where the noise in the data typically follows a Poisson distribution, we will show their performance for other applications such as photography, astronomical and microscopy imaging. More specifically, in the first part of the thesis we will focus on low dose CT data corrupted only by Poisson noise by extending automatic selection strategies designed for Gaussian noise and improving the few existing ones for Poisson. The new approaches will show to outperform the state-of-the-art competitors especially in the low-counting regime. Moreover, we will propose to extend the best performing strategy to the hard task of multi-parameter selection showing promising results. Finally, in the last part of the thesis, we will introduce the problem of material decomposition for hyperspectral CT, which data encodes information of how different materials in the target attenuate X-rays in different ways according to the specific energy. We will conduct a preliminary comparative study to obtain accurate material decomposition starting from few noisy projection data.