Numerical methods for dynamic Magnetic Resonance Imaging

Nel rapporto vengono presentati alcuni metodi nuemrici per la ricostruzione di immagini dinamiche di risonanza magnetica utilizzando anche informazioni a priori, attraverso una formula unificata che li descrive tutti. In particolare, si studia l'uso delle basi B-spline e della regolarizzazione nella ricostruzione di immagini dinamiche di risonanza magnetica

Uniform multi-penalty regularization for linear ill-posed inverse problems

This study examines, in the framework of variational regularization methods, a multi-penalty regularization approach which builds upon the Uniform PENalty (UPEN) method, previously proposed by the authors for Nuclear Magnetic Resonance (NMR) data processing. The paper introduces two iterative methods, UpenMM and GUpenMM, formulated within the Majorization-Minimization (MM) framework. These methods are designed to identify appropriate regularization parameters and solutions for linear inverse problems utilizing multi-penalty regularization. The paper demonstrates the convergence of these methods and illustrates their potential through numerical examples in one and two-dimensional scenarios, showing the practical utility of point-wise regularization terms in solving various inverse problems

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

Directional TGV-based image restoration under Poisson noise

We are interested in the restoration of noisy and blurry images where the texture mainly follows a single direction (i.e., directional images). Problems of this type arise, for example, in microscopy or computed tomography for carbon or glass fibres. In order to deal with these problems, the Directional Total Generalized Variation (DTGV) was developed by Kongskov et al. in 2017 and 2019, in the case of impulse and Gaussian noise. In this article we focus on images corrupted by Poisson noise, extending the DTGV regularization to image restoration models where the data fitting term is the generalized Kullback-Leibler divergence. We also propose a technique for the identification of the main texture direction, which improves upon the techniques used in the aforementioned work about DTGV. We solve the problem by an ADMM algorithm with proven convergence and subproblems that can be solved exactly at a low computational cost. Numerical results on both phantom and real images demonstrate the effectiveness of our approach.Comment: 20 pages, 1 table, 13 figure

ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration

We propose a method, called ACQUIRE, for the solution of constrained optimization problems modeling the restoration of images corrupted by Poisson noise. The objective function is the sum of a generalized Kullback-Leibler divergence term and a TV regularizer, subject to nonnegativity and possibly other constraints, such as flux conservation. ACQUIRE is a line-search method that considers a smoothed version of TV, based on a Huber-like function, and computes the search directions by minimizing quadratic approximations of the problem, built by exploiting some second-order information. A classical second-order Taylor approximation is used for the Kullback-Leibler term and an iteratively reweighted norm approach for the smoothed TV term. We prove that the sequence generated by the method has a subsequence converging to a minimizer of the smoothed problem and any limit point is a minimizer. Furthermore, if the problem is strictly convex, the whole sequence is convergent. We note that convergence is achieved without requiring the exact minimization of the quadratic subproblems; low accuracy in this minimization can be used in practice, as shown by numerical results. Experiments on reference test problems show that our method is competitive with well-established methods for TV-based Poisson image restoration, in terms of both computational efficiency and image quality.Comment: 37 pages, 13 figure

Inter-society consensus for the use of inhaled corticosteroids in infants, children and adolescents with airway diseases

Background: In 2019, a multidisciplinary panel of experts from eight Italian scientific paediatric societies developed a consensus document for the use of inhaled corticosteroids in the management and prevention of the most common paediatric airways disorders. The aim is to provide healthcare providers with a multidisciplinary document including indications useful in the clinical practice. The consensus document was intended to be addressed to paediatricians who work in the Paediatric Divisions, the Primary Care Services and the Emergency Departments, as well as to Residents or PhD students, paediatric nurses and specialists or consultants in paediatric pulmonology, allergy, infectious diseases, and ear, nose, and throat medicine. Methods: Clinical questions identifying Population, Intervention(s), Comparison and Outcome(s) were addressed by methodologists and a general agreement on the topics and the strength of the recommendations (according to the GRADE system) was obtained following the Delphi method. The literature selection included secondary sources such as evidence-based guidelines and systematic reviews and was integrated with primary studies subsequently published. Results: The expert panel provided a number of recommendations on the use of inhaled corticosteroids in preschool wheezing, bronchial asthma, allergic and non-allergic rhinitis, acute and chronic rhinosinusitis, adenoid hypertrophy, laryngitis and laryngospasm. Conclusions: We provided a multidisciplinary update on the current recommendations for the management and prevention of the most common paediatric airways disorders requiring inhaled corticosteroids, in order to share useful indications, identify gaps in knowledge and drive future research