Analisi di strutture nella ricostruzione di immagini e monumenti

1. Definizione ed analisi teorica di nuovi operatori di proiezione per metodi multigrid basati solo sulle informazioni algebriche del problema, applicabili sia a discretizzazioni agli elementi finiti, sia a problemi di ricostruzione di immagini ed a matrici di grafo. 2. Definizione e studio di metodi multilivello regolarizzanti per la ricostruzione di immagini sfocate ed affette da rumore, combinando tecniche nonlineari di edge-preserving con operatori di trasferimento di griglia regolarizzanti che preservano la struttura. 3. Applicazione di condizioni al contorno in grado di preservare segnali smooth a tecniche di regolarizzazione accurate e solitamente computazionalmente costose, (e.g., Total Variation (TV), Regularized Total Least Square (RTLS), preconditioned GMRES, etc.), ricorrendo a trasformate discrete veloci di recente sviluppo (generalizzazione di FFT). 4. Studio di metodi impliciti per EDP paraboliche degeneri con applicazioni sia ai modelli di degrado monumentale sia a problemi di ricostruzione di immagini sfocate con termine regolarizzante non lineare. 5. Analisi spettrale di matrici, con struttura nascosta, non Hermitiane associate a simboli a blocchi con applicazioni al precondizionamento di EDP, alla regolarizzazione non lineare, ed a problemi di ricostruzione di segnali o immagini in cui alcuni campionamenti non sono disponibili o in cui le dimensioni del dominio introducono evidenti distorsioni di tipo prospettico

Potential Response of Soil-Borne Fungal Pathogens Affecting Crops to a Scenario of Climate Change in Europe

A study was carried out on the potential response of soil-borne pathogens causing crop yield losses under a climate change scenario in Europe. A controlled chamber set of experiments was carried out to quantify pathogen response to temperature using pure colonies of three soil-borne fungi, representative of low (Fusarium nivale), medium-high (Athelia rolfsii) and high (Macrophomina phaseolina) temperature requirements. A generic model to simulate fungal growth response to temperature based on these experiments was developed and linked to a soil temperature model component, and to components to simulate soil water content accounting for crop water uptake of potential hosts. Pathogens relative growth was simulated over Europe using the IPCC A1B emission scenario as realization of the Hadley-CM3 global climate model, available from the European Commission and processed for use with biophysical models. The simulations resulting from using the time span centred on 2030 were compared to the baseline, centred on the year 2000, using a sample of 30 years of daily weather. The general trend of soil-borne pathogens response to the scenario of climate change is a relative increase in growth in colder areas of Europe, as a function of their temperature requirements. Projections of F. nivale in the future indicate a relative increase of this winter pathogen of wheat in Northern European countries. A. rolfsii and M. phaseolina, two soil-borne pathogens typical of warmer agricultural areas, could find more favourable conditions in areas of the Central Europe, but they differentiated in Southern Europe where A. rolfsii resulted affected by summer soil temperatures above optimum

On the regularizing power of multigrid-type algorithms

We consider the deblurring problem of noisy and blurred images in the case of known space invariant point spread functions with four choices of boundary conditions. We combine an algebraic multigrid previously defined ad hoc for structured matrices related to space invariant operators (Toeplitz, circulants, trigonometric matrix algebras, etc.) and the classical geometric multigrid studied in the partial differential equations context. The resulting technique is parameterized in order to have more degrees of freedom: a simple choice of the parameters allows us to devise a quite powerful regularizing method. It defines an iterative regularizing method where the smoother itself has to be an iterative regularizing method (e.g., conjugate gradient, Landweber, conjugate gradient for normal equations, etc.). More precisely, with respect to the smoother, the regularization properties are improved and the total complexity is lower. Furthermore, in several cases, when it is directly applied to the system $A{\bf f}={\bf g}$, the quality of the restored image is comparable with that of all the best known techniques for the normal equations $A^TA{\bf f}=A^T{\bf g}$, but the related convergence is substantially faster. Finally, the associated curves of the relative errors versus the iteration numbers are ``flatter'' with respect to the smoother (the estimation of the stop iteration is less crucial). Therefore, we can choose multigrid procedures which are much more efficient than classical techniques without losing accuracy in the restored image (as often occurs when using preconditioning). Several numerical experiments show the effectiveness of our proposals

1911 Old Home Week Sheet Music

Original sheet music from the 1911 Brockport Old Home Week Celebration.https://digitalcommons.brockport.edu/local_books/1004/thumbnail.jp

Theoretical and numerical aspects of a non-stationary preconditioned iterative method for linear discrete ill-posed problems

This work considers some theoretical and computational aspects of the recent paper (Buccini et al., 2021), whose aim was to relax the convergence conditions in a previous work by Donatelli and Hanke, and thereby make the iterative method discussed in the latter work applicable to a larger class of problems. This aim was achieved in the sense that the iterative method presented convergences for a larger class of problems. However, while the analysis presented is correct, it does not establish the superior behavior of the iterative method described. The present note describes a slight modification of the analysis that establishes the superiority of the iterative method. The new analysis allows to discuss the behavior of the algorithm when varying the involved parameters, which is also useful for their empirical estimation

Fractional graph Laplacian for image reconstruction

Image reconstruction problems, like image deblurring and computer tomography, are usually ill-posed and require regularization. A popular approach to regularization is to substitute the original problem with an optimization problem that minimizes the sum of two terms, an term and an term with . The first penalizes the distance between the measured data and the reconstructed one, the latter imposes sparsity on some features of the computed solution. In this work, we propose to use the fractional Laplacian of a properly constructed graph in the term to compute extremely accurate reconstructions of the desired images. A simple model with a fully automatic method, i.e., that does not require the tuning of any parameter, is used to construct the graph and enhanced diffusion on the graph is achieved with the use of a fractional exponent in the Laplacian operator. Since the fractional Laplacian is a global operator, i.e., its matrix representation is completely full, it cannot be formed and stored. We propose to replace it with an approximation in an appropriate Krylov subspace. We show that the algorithm is a regularization method under some reasonable assumptions. Some selected numerical examples in image deblurring and computer tomography show the performance of our proposal

Late thoracic pseudo-aneurysm causing collapse of vascular prostheses

The outcome of patients with thoracic vascular prostheses is usually uneventful. We report two cases of collapse of thoracic vascular prostheses which occurred ten and forty years, respectively, after the implantation. The diagnoses were obtained preoperatively by CT-scan or NMR and angiography. Both patients were successfully treated with prosthetic replacement by an open approach