Applications of PDEs inpainting to magnetic particle imaging and corneal topography
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 analys...
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doaj-2c0c54fadd1d490780d6e5aede77b9ad2020-11-24T21:45:06ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742019-01-01394453482https://doi.org/10.7494/OpMath.2019.39.4.4533928Applications of PDEs inpainting to magnetic particle imaging and corneal topographyAndrea Andrisani0https://orcid.org/0000-0002-7603-8537Rosa Maria Mininni1https://orcid.org/0000-0002-0230-1435Francesca Mazzia2https://orcid.org/0000-0003-1072-9578Giuseppina Settanni3https://orcid.org/0000-0002-9954-5371Alessandro Iurino4Sabina Tangaro5https://orcid.org/0000-0002-1372-3916Andrea Tateo6https://orcid.org/0000-0001-9570-0277Roberto Bellotti7https://orcid.org/0000-0003-3198-2708Università degli Studi di Bari Aldo Moro, Dipartimento di Matematica, 70125 Bari, ItalyUniversità degli Studi di Bari Aldo Moro, Dipartimento di Matematica, 70125 Bari, ItalyUniversità degli Studi di Bari Aldo Moro, Dipartimento di Informatica, 70125 Bari, ItalyUniversità degli Studi di Bari Aldo Moro, Dipartimento di Matematica, 70125 Bari, ItalyUniversità degli Studi di Bari Aldo Moro, Dipartimento Interateneo di Fisica "M. Merlin", 70125 Bari, ItalyIstituto Nazionale di Fisica Nucleare, sezione di Bari, 70125 Bari, ItalyUniversità degli Studi di Bari Aldo Moro, Dipartimento Interateneo di Fisica "M. Merlin", 70125 Bari, ItalyUniversità degli Studi di Bari Aldo Moro, Dipartimento Interateneo di Fisica "M. Merlin", 70125 Bari, ItalyIn 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.https://www.opuscula.agh.edu.pl/vol39/4/art/opuscula_math_3928.pdfpdes inpaintingmedical imagingmagnetic particle imagingradial curvature imageanterior surface of a cornea |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Andrea Andrisani Rosa Maria Mininni Francesca Mazzia Giuseppina Settanni Alessandro Iurino Sabina Tangaro Andrea Tateo Roberto Bellotti |
spellingShingle |
Andrea Andrisani Rosa Maria Mininni Francesca Mazzia Giuseppina Settanni Alessandro Iurino Sabina Tangaro Andrea Tateo Roberto Bellotti Applications of PDEs inpainting to magnetic particle imaging and corneal topography Opuscula Mathematica pdes inpainting medical imaging magnetic particle imaging radial curvature image anterior surface of a cornea |
author_facet |
Andrea Andrisani Rosa Maria Mininni Francesca Mazzia Giuseppina Settanni Alessandro Iurino Sabina Tangaro Andrea Tateo Roberto Bellotti |
author_sort |
Andrea Andrisani |
title |
Applications of PDEs inpainting to magnetic particle imaging and corneal topography |
title_short |
Applications of PDEs inpainting to magnetic particle imaging and corneal topography |
title_full |
Applications of PDEs inpainting to magnetic particle imaging and corneal topography |
title_fullStr |
Applications of PDEs inpainting to magnetic particle imaging and corneal topography |
title_full_unstemmed |
Applications of PDEs inpainting to magnetic particle imaging and corneal topography |
title_sort |
applications of pdes inpainting to magnetic particle imaging and corneal topography |
publisher |
AGH Univeristy of Science and Technology Press |
series |
Opuscula Mathematica |
issn |
1232-9274 |
publishDate |
2019-01-01 |
description |
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. |
topic |
pdes inpainting medical imaging magnetic particle imaging radial curvature image anterior surface of a cornea |
url |
https://www.opuscula.agh.edu.pl/vol39/4/art/opuscula_math_3928.pdf |
work_keys_str_mv |
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