Positron emission tomography (PET), is a medical imaging technique that provides functional information about physiological processes. The goal of PET is to reconstruct the distribution of the radioisotopes in the body by measuring the emitted photons. The computer methods are designed to solve the inverse problem known as "image reconstruction from projections." In this paper, an iterative image reconstruction algorithm ART was regularized by combining Tikhonov and total variation regularizations. In the first step, combined regularization algorithm of total variation and Tikhonov regularization was applied to the image obtained by ART algorithm in each iteration for background noise removal with preserving edges. The quality measurements and visual inspections show a significant improvement in image quality compared to other algorithms.
In this paper we study continuum limits of the discretized [[EQUATION]] -Laplacian evolution problem on sparse graphs with homogeneous Neumann boundary conditions. This goes far beyond known results by handling much more general class of kernels, possibly singular, and graph sequences whose limit are the so-called [[EQUATION]] -graphons. More precisely, we derive a bound on the distance between two continuous-in-time trajectories defined by two different evolution systems (i.e. with different kernels, second member and initial data). Similarly, we provide a bound in the case that one of the trajectories is discrete-in-time and the other is continuous. In turn, these results lead us to establish error estimates of the full discretization of the [[EQUATION]] -Laplacian problem on sparse random graphs. In particular, we provide rate of convergence of solutions for the discrete models to the solution of the continuous problem as the number of vertices grows.
Imagerie numérique et patrimoine culturel : enjeux scientifiques et opérationnels La reconstruction du panorama de la « Tapisserie de Bayeux » comme fond de référence d'un système d'information documentaire spatialisée Algorithmes de traitement d'images dédiés à la construction d'un panorama et au recalage d'images sur le panorama The reconstruction of the Bayeux tapestry panorama as a reference tool for a spatialised system of documentary information. Image-processing algorithms devoted to panorama construction and plotting of images on this panorama
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