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Last name: BRIANZI
First name: Paola
In this paper we consider the problem of Laplace transform inversion in the case where the transform is given in a set of equidistant points. We propose a criterion, based on cross-validation, for the optimal choice of the first data point.
The paper present an algorithm for the regularized inversion of the Laplace transform. The authors assume that the values of the Laplace transform are given in a finite number of equidistant points and that these values are affected by gaussian noise.
This paper deals with the problem of reconstructing a band-limited signal when a nite subset of its samples and of its derivative are missing. The technique used, due to P.J.S.G. Ferreira, is based on the use of a particular frame for band-limited functions and the relative oversampling formulas. We study the eigenvalues of the matrices arising...
We apply the natural pixel (NP) approach to the single photon emission computed tomography (SPECT) problem. The rotational invariance of the system induces a block circulant structure in the Gram matrix. This structure can be used to reduce the computational efforts needed for solving the inverse problem.
The Landweber method is a simple and flexible iterative regularization algorithm, whose projected variant provides nonnegative image reconstructions. Since the method is usually very slow, we apply circulant preconditioners, exploiting the shift invariance of many deblurring problems, in order to accelerate the convergence. This way reasonable...
Regularization methods for inverse problems formulated in Hilbert spaces usually give rise to over-smoothness, which does not allow to obtain a good contrast and localization of the edges in the context of image restoration. On the other hand, regularization methods recently introduced in Banach spaces allow in general to obtain better...
We present mathematical and numerical models for SPECT imaging, as an example of application where a description in terms of structured matrices seems attractive for reducing the high complexity of the reconstruction problem. We discuss how structures can be incorporated in the models and we suggest some computational techniques in order to...
Krylov subspace iterative methods have recently received considerable attention as regularizing techniques for solving linear systemswith a coefficient matrix of ill-determined rank and a right-hand side vector perturbed by noise. For many of them little is known from this point of view. In this paper, the regularizing properties of some...
La ricostruzione accurata di dati SPECT richiede una modellizzazione completamente tridimensionale (3D) del blurring del collimatore, modellizzazione che va poi inserita in un algoritmo iterativo. Purtroppo il costo computazionale di questa strategia e' estremamente elevato e questo fatto ne impedisce la diffusione nell'ambiente clinico. In...
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