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Browsing by Author "Mazzia, Francesca"

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    Item type:Article, Access status: Open Access ,
    Applications of PDEs inpainting to magnetic particle imaging and corneal topography
    (Wydawnictwa AGH, 2019) Andrisani, Andrea; Mininni, Rosa Maria; Mazzia, Francesca; Settanni, Giuseppina; Iurino, Alessandro; Tangaro, Sabina; Tateo, Andrea; Bellotti, Roberto
    In this work we propose a novel application of Partial Differential Equations (PDEs) inpainting techniques to two medical contexts. The first one concerning recovering of concentration maps for superparamagnetic nanoparticles, used as tracers in the framework of Magnetic Particle Imaging. The analysis is carried out by two set of simulations, with and without adding a source of noise, to show that the inpainted images preserve the main properties of the original ones. The second medical application is related to recovering data of corneal elevation maps in ophthalmology. A new procedure consisting in applying the PDEs inpainting techniques to the radial curvature image is proposed. The images of the anterior corneal surface are properly recovered to obtain an approximation error of the required precision. We compare inpainting methods based on second, third and fourth-order PDEs with standard approximation and interpolation techniques.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Solving boundary value problems in the open source software R - package bvpSolve
    (2014) Mazzia, Francesca; Cash, Jeff R.; Soetaert, Karline
    The R package bvpSolve for the numerical solution of Boundary Value Problems (BVPs) is presented. This package is free software which is distributed under the GNU General Public License, as part of the R open source software project. It includes some well known codes to solve boundary value problems of ordinary differential equations (ODEs) and differential algebraic equations (DAEs). In addition to the packages already available for solving initial value problems, the new package now allows non expert users to efficiently solve boundary value problems in the problem solving environment R.