An Automatic Pixel-Wise Multi-Penalty Approach to Image Restoration.

This work tackles the problem of image restoration, a crucial task in many fields of applied sciences, focusing on removing degradation caused by blur and noise during the acquisition process. Drawing inspiration from the multi-penalty approach based on the Uniform Penalty principle, discussed in previous work, here we develop a new image restoration model and an iterative algorithm for its effective solution. The model incorporates pixel-wise regularization terms and establishes a rule for parameter selection, aiming to restore images through the solution of a sequence of constrained optimization problems. To achieve this, we present a modified version of the Newton Projection method, adapted to multi-penalty scenarios, and prove its convergence. Numerical experiments demonstrate the efficacy of the method in eliminating noise and blur while preserving the image edges.

Switched forced SEIRDV compartmental models to monitor COVID-19 spread and immunization in Italy.

This paper presents a new hybrid compartmental model for studying the COVID-19 epidemic evolution in Italy since the beginning of the vaccination campaign started on 2020/12/27 and shows forecasts of the epidemic evolution in Italy in the first six months. The proposed compartmental model subdivides the population into six compartments and extends the SEIRD model proposed in [E.L.Piccolomini and F.Zama, PLOS ONE, 15(8):1-17, 08 2020] by adding the vaccinated population and framing the global model as a hybrid-switched dynamical system. Aiming to represent the quantities that characterize the epidemic behaviour from an accurate fit to the observed data, we partition the observation time interval into sub-intervals. The model parameters change according to a switching rule depending on the data behaviour and the infection rate continuity condition. In particular, we study the representation of the infection rate both as linear and exponential piecewise continuous functions. We choose the length of sub-intervals balancing the data fit with the model complexity through the Bayesian Information Criterion. We tested the model on italian data and on local data from Emilia-Romagna region. The calibration of the model shows an excellent representation of the epidemic behaviour in both cases. Thirty days forecasts have proven to well reproduce the infection spread, better for regional than for national data. Both models produce accurate predictions of infected, but the exponential-based one perform better in most of the cases. Finally, we discuss different possible forecast scenarios obtained by simulating an increased vaccination rate.

A New Hybrid Inversion Method for 2D Nuclear Magnetic Resonance Combining TSVD and Tikhonov Regularization.

This paper is concerned with the reconstruction of relaxation time distributions in Nuclear Magnetic Resonance (NMR) relaxometry. This is a large-scale and ill-posed inverse problem with many potential applications in biology, medicine, chemistry, and other disciplines. However, the large amount of data and the consequently long inversion times, together with the high sensitivity of the solution to the value of the regularization parameter, still represent a major issue in the applicability of the NMR relaxometry. We present a method for two-dimensional data inversion (2DNMR) which combines Truncated Singular Value Decomposition and Tikhonov regularization in order to accelerate the inversion time and to reduce the sensitivity to the value of the regularization parameter. The Discrete Picard condition is used to jointly select the SVD truncation and Tikhonov regularization parameters. We evaluate the performance of the proposed method on both simulated and real NMR measurements.

Monitoring Italian COVID-19 spread by a forced SEIRD model.

Due to the recent evolution of the COVID-19 outbreak, the scientific community is making efforts to analyse models for understanding the present situation and for predicting future scenarios. In this paper, we propose a forced Susceptible-Exposed-Infected-Recovered-Dead (fSEIRD) differential model for the analysis and forecast of the COVID-19 spread in Italian regions, using the data from the Italian Protezione Civile (Italian Civil Protection Department) from 24/02/2020. In this study, we investigate an adaptation of fSEIRD by proposing two different piecewise time-dependent infection rate functions to fit the current epidemic data affected by progressive movement restriction policies put in place by the Italian government. The proposed models are flexible and can be quickly adapted to monitor various epidemic scenarios. Results on the regions of Lombardia and Emilia-Romagna confirm that the proposed models fit the data very accurately and make reliable predictions.