Opuscula Math. 39, no. 4 (2019), 453-482

Opuscula Mathematica

Applications of PDEs inpainting to magnetic particle imaging and corneal topography

Andrea Andrisani
Rosa Maria Mininni
Francesca Mazzia
Giuseppina Settanni
Alessandro Iurino
Sabina Tangaro
Andrea Tateo
Roberto Bellotti

Abstract. 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.

Keywords: PDEs inpainting, medical imaging, magnetic particle imaging, radial curvature image, anterior surface of a cornea.

Mathematics Subject Classification: 35Q68, 68U10, 82D80, 92C55, 94A08.

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  • Alessandro Iurino
  • Università degli Studi di Bari Aldo Moro, Dipartimento Interateneo di Fisica "M. Merlin", 70125 Bari, Italy
  • Roberto Bellotti
  • ORCID iD https://orcid.org/0000-0003-3198-2708
  • Università degli Studi di Bari Aldo Moro, Dipartimento Interateneo di Fisica "M. Merlin", 70125 Bari, Italy
  • Istituto Nazionale di Fisica Nucleare, sezione di Bari, 70125 Bari, Italy
  • Communicated by Zdzisław Jackiewicz.
  • Received: 2019-01-15.
  • Accepted: 2019-01-29.
  • Published online: 2019-05-23.
Opuscula Mathematica - cover

Cite this article as:
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 Math. 39, no. 4 (2019), 453-482, https://doi.org/10.7494/OpMath.2019.39.4.453

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